Bennett, lying in his hospital bed in Washington, D.C., earlier this month after suffering a stroke, asked his son, Jim, and wife, Joyce, if there were any Muslims in the hospital.
Late last year, Trump called for a "complete shutdown" of Muslims entering the United States until "our country's representatives can figure out what is going on." He later clarified in a phone interview on "Good Morning America" that Muslim U.S. citizens will be allowed back in the country.
Trump has since said that his controversial plan to ban most Muslims from entering the U.S. is "just a suggestion."
"I don't remember if I said anything, but I was intensely proud of him," Jim, a freelance writer, told ABC News of his father and his response to their conversation, which was first reported by The Daily Beast.
"We didn't follow through with it, but that was what was on his mind," Joyce said.
Bennett, who served as Utah's longtime junior senator until losing his seat in the 2010 Tea Party wave to Sen. Mike Lee, R-Utah, had closely followed this year's GOP presidential primary.
The Utah Republican, known for working across the aisle in the Senate, told the Washington Post last July that Trump would "self-destruct relatively quickly."
"The dynamic, I think, will change very dramatically, and Trump will be yesterday's news," he told the paper. "But if this does have legs, if Trump can keep this going, it will be very worrisome."
He had also been concerned about Trump's rhetoric toward Muslims before he was hospitalized, according to Joyce.
"I saw him stop someone in an airport, because we were traveling, saying, 'We're glad you're in our country, you're welcome here,'" she recalled.
Bennett died on May 4 at the age of 82. He had been battling pancreatic cancer.