A Fox host he routinely watches said Tuesday he should "set a good example."
It comes as Vice President Mike Pence, facing reporters, claimed the president has been clear in his support of masks, even saying he's worn one in public -- which he has not.
"Unfortunately, this simple life-saving practice has become part of the political debate that says this: if you're for Trump, you don't wear a mask; if you're against Trump, you do," Alexander said as he chaired a Senate hearing on the state of the crisis with Dr. Anthony Fauci and other health experts.
He pointed to Centers for Disease Control and Prevention research showing wearing a mask significantly slows the spread.
"That's why I've suggested that the president occasionally wear a mask, even though in most cases, it's not necessary for him to do so," he added. "The president has plenty of admirers. They would follow his lead."
Alexander joins a growing chorus of calls from congressional Republicans, including Senate Majority Leader Mitch McConnell, to wear masks.
Sen. Lisa Murkowski, R-Alaska, said she thought it would be helpful if Trump would wear one.
"I think that we all should be wearing masks, and I think it would help if the president were to do so as well I think that that says that we all have a level of personal responsibility," Murkowski said.
And a similar plea came from Sen. Mitt Romney, R-Utah, the only Republican senator who voted to to remove Trump from office.
"If the president wants to make clear that he is fully supportive of people wearing masks, that would be very helpful," Romney said Tuesday.
Even Trump allies at Fox News are sending the message.
"Fox and Friends" co-host Steve Doocy on Tuesday morning said it would set "a good example" for Trump to use one.
"He'd be a good role model. I don't see any downside to the president wearing a mask in public," the conservative-host said during an interview Republican National Committee Chair Ronna McDaniel.
"'MAGA' should now stand for 'Masks Are Great Again.' Let me give you some marketing advice right there," he added.
Fox host Sean Hannity, too, whom Trump has called one of "favorite journalists," also suggested Monday night more Americans should consider wearing them.
"I went to my grocery store every week. Guess what? They wore masks. Nobody at my grocery store, thank God, got coronavirus," Hannity said. "I think they work."
"And I said -- especially if I wear a mask and it opens up baseball, concerts, NFL football -- I'd rather wear the mask and go to the game to protect Grandpa, Grandma, Ma and Dad, and watch the ball game."
The abrupt shift in conservative thought reflects both overwhelming public opinion and scientific studies that masks are effective in slowing the spread of the virus -- but it stands in clear contradiction to President Trump's messaging.
White House press secretary Kayleigh McEnany on Monday, asked if Trump would wear one at the Republican National Convention in Jacksonville, Florida, in August since the city made them mandatory in public, said it's "his choice" to wear a mask even as he recommended others follow guidance of state and local officials.
"I talked to the president before coming out here," McEnany said. "It's his choice to wear a mask. It's the personal choice of any individual as to whether to wear a mask or not. He encourages people to make whatever decision is best for their safety, but he did say to me he has no problem with masks, and to do whatever your local jurisdiction requests of you."
Fauci and other top health officials at the Senate hearing sung the praises of masks as Fauci warned the U.S. could see 100,000 cases a day if the country doesn't get the spread under control.
"Yes, of course," Fauci said. "Anything that furthers the use of mask, whether it's giving out free masks, any other mechanism, I am thoroughly in favor of."
CDC Director Dr. Robert Redfield added: "It is critical that we all take the personal responsibility to slow the transmission of COVID-19 and embrace the universal use of face coverings."
While the hearing was underway, former Vice President Joe Biden, Trump's presumptive political opponent in November, in a campaign speech Tuesday called the president's response the coronavirus crisis a failure and used masks as an example of how he's divided the country over the pandemic.
"We can't continue half wearing masks and half-rejecting science," Biden said. "Wear a mask, keep your distance, limit the size of crowds. Mr. President, this is not about you. It's about the health and well being of the American public."
While Trump and Biden present their conflicting leadership styles to the American people, financial institutions are also weighing in what's become a political issue.
Goldman Sachs chief economist, Jan Hatzius, said his team investigated the link between face masks and COVID-19 health and economic outcomes and found a national mask mandate could save the country from a huge economic hit -- a point that may grab Trump's attention.
"These calculations imply that a face mask mandate could potentially substitute for lockdowns that would otherwise subtract nearly 5% from GDP," the economist wrote in a note to clients.
Though the CDC first recommended face masks or covering for Americans on April 3, some studies have since found if masks had been mandated earlier lives could have been saved.
The Institute for Health Metrics and Evaluation's (IHME) model, often cited by the White House, predicts that more than 175,000 people in the U.S. will die from COVID-19 by Oct. 1. That number would drops by tens of thousands to 146,000 deaths if 95% of the population wore a mask or covering around others.
Pence, head of the coronavirus task force, has also urged more Americans to wear masks in the last few days, repeating several times at a coronavirus task force briefing Tuesday: "Wear a mask."
Questioned by ABC's John Parkinson about the president's reluctance to wear one, Pence replied: "Well, the president's worn a mask in public, as have I. And you've heard a strong encouragement, about mask wearing."
The vice president's reference wasn't immediately clear.
During a visit in to a Ford plant in Detroit in late May, President Trump said he "wore one in the back area" but not openly because he "didn't want to give the press the pleasure of seeing it."
Pence went on to paint the administration as being clear in its message on masks, even as Trump has not conveyed it himself.
The vice president has stepped up his rhetoric around masks significantly since Sunday, when he visited the hotspot state of Texas and said, "Wearing a mask is just a good idea."
Hours earlier, Pence spoke at a mega-church in Dallas with over 2,000 congregants and a 100-person choir -- standing close and none wearing masks while singing -- though the CDC has warned of the "super spreader" potential.
Even as more states and cities adopt mask mandates citing public health and safety, not all Republicans are on board with the science.
Sen. Rand Paul, R-Ky., who graduated from Duke University Medical School, said in the coronavirus hearing Tuesday: "We shouldn't presume that a group of experts somehow knows what's best for everyone."
Republican Gov. Kristi Noem of South Dakota told Fox News Monday night "we won't be social distancing" at Trump's Fourth of July celebration at Mount Rushmore.
Noem added that while the state would provide masks to those attending the Friday evening event, it would not require people to wear them.
ABC News' Anne Flaherty, Trish Turner, Allison Pecorin, Jordyn Phelps, John Parkinson and Catherine Thorbecke contributed to this report.