Transition sources say Trump is still considering a number of different candidates, from Trump loyalists to retired military officials, ahead of a self-imposed goal of the end of the week to finalize his cabinet.
A senior Trump transition official says the president-elect has also interviewed retired Gen. Ann Dunwoody, who served as the Army’s first female four-star general.
Hegseth, who is an Army veteran and Fox News contributor, has met with Trump twice, most recently on Thursday at Trump Tower.
One senior transition official told ABC News the position of VA secretary is proving to be the "most difficult" cabinet position to fill.
Trump's pick will be responsible for managing the government’s second-largest department and a national health care system that serves more than 6.6 million veterans and beneficiaries each year.
Some veterans’ advocacy groups have expressed frustration that Trump has not met personally with them to discuss the selection, instead meeting with a mix of celebrities and CEOs.
Asked about Trump's focus on selecting a VA secretary, transition officials say the president-elect is taking the issue seriously.
"This is an area he cares deeply about, reforming the VA," spokesman Sean Spicer said on a call with reporters Thursday. He said that this is "an area that's near and dear to his heart and one that he really wants to make sure is addressed appropriately, quickly and successfully."
"Transforming an agency as large and diverse as VA will take a continuous commitment from leadership over the course of many years," a coalition of 20 veterans groups wrote in a letter to Trump and the transition team. "As you make your selection for VA Secretary, then, we advocate for an approach that recognizes and builds upon current progress. Given the challenges we face, we cannot afford to start over."
Trump has proposed making it easier for secretaries to fire VA employees, creating a commission to investigate fraud in the agency and creating a 24/7 White House hotline for veterans' complaints.
In interviews, top veterans' advocates say Trump has much in common with McDonald, a registered Republican and former CEO of Proctor & Gamble.
"They’re both businessmen from outside the government that have a different perspective," said Garry Augustine, the executive director of Disabled American Veterans. "If he wasn’t already secretary, president-elect Trump would probably be looking at him."
Bill Rausch, the executive director of Got Your 6, said keeping McDonald would allow the Trump administration to hit the ground running in January to pass reforms with a GOP-led Congress.
"If we bring in a new VA leader who is going to take a year, two years to get up to speed," he said. "We could miss that window of opportunity."
It’s not clear if McDonald and Trump have been in contact with each other, but those who have spoken to the current secretary said he would consider serving in a Trump administration.
McDonald told the Military Times in a recent interview that he has not been approached about serving in the Trump administration.
“I have not been approached, and I’m making plans according to that. But service is important," he said.
ABC News' request for comment from McDonald’s office was not immediately returned.
"I think he would say yes," Rausch said. "His answer has been that he’s a member of the Veterans Party and he’ll do what’s best for veterans."