There will be no Aaron Rodgers/Jordan Love-like drama in Tampa ... 'cause new Bucs rookie QB Kyle Trask says Tom Brady's already offering to be his mentor!!

The former Univ. of Florida signal-caller -- who was drafted in the 2nd-round by Tampa Bay last week -- says Brady is already looking to meet him, throw with him and take him under his wing.

“He actually did reach out to me a couple of days after the draft," Trask said of Brady to NFL Network.