The 43-year-old quarterback signed a two-year deal with the NFC South club last offseason after leaving the New England Patriots.
After Brady talked about possibly playing beyond age 45 prior to Tampa Bay's Super Bowl win over the Kansas City Chiefs, Licht hopes their partnership will continue.
"That's a possibility," Licht told "The Rich Eisen Show" about Brady signing an extension. "He certainly didn't look like he slowed down any this year. So, that's a possibility. We'll have to see how that goes."
"I talk to Tom often," he added. "Probably keep that under wraps right now. It appears that he really had a good time this year winning the Super Bowl. Likes our organization, likes our coaches, likes our head coach, and ownership. And we certainly love him. Usually, when you have those things going for each other, it's a match made in happen, so we'd like to keep this going."
Bucs head coach Bruce Arians also suggested before the Super Bowl that Brady could ink a new deal after enjoying his first season outside of New England.
"I think Tom's real happy with where he's at, and I wouldn't be surprised," said Arians.
Brady rebounded from a poor final season with the Patriots to throw for the second-most touchdowns of his career (40) and the league's third-most passing yards (4,633).
Brady's $28.4-million cap hit in 2021 is by far the team's largest, according to Spotrac.
The Buccaneers could suggest an extension this offseason to help lower the quarterback's cap number, and then use the extra space to retain the club's championship core.