Suh would replace Gerald McCoy, who was released by the Buccaneers on Monday. Suh (second) and McCoy (third) were taken with consecutive picks in the first round of the 2010 NFL draft.
Suh was interested in playing for Tampa's new defensive coordinator Todd Bowles, the source said.
Bucs head coach Bruce Arians was asked about Suh earlier on Tuesday.
"I can't talk about him. He's not on my team,'' Arians said.
After being reminded that Suh is a free agent and he can talk about him without fear of tampering violations, Arians said: "He's a hell of a player, so we'll see.''
McCoy, 31, a six-time Pro Bowler and arguably the Bucs' most visible player over the past nine seasons on and off the field, had been a no-show for the Bucs' offseason program that began last month.
The source of contention was McCoy's $13 million salary in 2019, none of which was guaranteed. He had three years currently remaining on his deal, which would have kept him with the team through 2021.
The Los Angeles Rams signed Suh to a one-year contract worth $14 million last March following his release from the Miami Dolphins. Suh chose the Rams among several suitors, including the New Orleans Saints, Tennessee Titans and Oakland Raiders, and said he made his decision, in part, because of the Rams' immediate ability to make a playoff run.
Playing alongside two-time NFL Defensive Player of the Year Aaron Donald, Suh did not make a significant impact until the playoffs. He finished the regular season with 4.5 sacks, four pass deflections and two fumble recoveries.
But the 6-foot-4, 305-pound defensive tackle was dominant in helping to shut down running back Ezekiel Elliott in a divisional-round win over the Dallas Cowboys and continued to prove his worth in a victory over the New Orleans Saints in the NFC Championship Game, when he had 1.5 sacks and four tackles.
Suh, 32, was selected second overall by the Detroit Lions in 2010. He played five seasons in Detroit and was named a four-time Pro Bowl selection and three-time All Pro.
In 2015, Suh signed a six-year, $114 million contract, with $60 million guaranteed, with the Miami Dolphins to become the highest-paid defensive player in NFL history. In three seasons with the Dolphins, Suh recorded 15.5 sacks and forced two fumbles.
Suh has 56 career sacks and in nine seasons has missed only two starts, both in 2011, when the NFL suspended him two games for on-field conduct.
ESPN's Jenna Laine and Lindsey Thiry contributed to this report.