Jennings said that after a short nap, coach Lovie Smith asked him to return to the Bucs facility "just to hang around the guys."
"It was good to see some of my former [Chicago Bears] teammates, from Henry [Melton], Major [Wright] and Chris [Conte]," Jennings said.
Jennings said there's an obvious comfort level if things work out with the Bucs, as he already knows Smith's defensive scheme from his days in Chicago, and Jennings feels he can slip right in.
The Bears announced the release of the 31-year-old Jennings on Sunday. A 10-year veteran, the two-time Pro Bowler had seen his role diminish in Chicago in recent weeks.
Jennings told Anderson his process of selecting a team is not all about judging the championship caliber of a team. Jennings also welcomes the opportunity to help develop younger players.
As for when Jennings will make a decision, he said: "I want to sleep on it. I do want to take this time to see what other opportunities may materialize, if possible. Some teams may have some things come up with more roster cuts. Obviously I also have a strong connection to Tampa too. So we will see."
ESPN.com's Jeff Dickerson contributed to this report.