Tagovailoa was taken in the first round of the 2020 NFL Draft by the Miami Dolphins and Smith could follow suit this April.
"We just talked about it, talking about (how) it'd be nice to run it back again," Smith said on NFL Network after Tuesday's Senior Bowl practice. "Not too much, but somewhat talked about it."
The Dolphins own the third overall pick and the No. 18 selection in this year's draft and could pair their franchise quarterback with a weapon he has proven chemistry with.
The duo won a national championship in 2017 when Tagovailoa came in off the bench and fired a 41-yard touchdown bomb to Smith to win the game in overtime.
Smith, the 2020 Heisman Trophy winner, has been working with the Dolphins' coaching staff at the Senior Bowl.
"This guy is a very good player," Dolphins head coach Brian Flores said, according to ESPN's Cameron Wolfe. "He made a lot of plays in college. He made a lot of plays in the biggest games of the year. You can nitpick all day on things on people. He's a very good player, and it's been good getting to know him. He's a good kid, too."