Kelly is interested in leaving Oregon, and the Bucs are working to cement a deal with him. He would replace Raheem Morris, who was fired after a 4-12 season.
KGW-TV in Portland, Ore., and the Tampa Bay Times reported that the sides are in the process of finalizing a deal.
Kelly met with general manager Mark Dominik and members of the Bucs' ownership group this past week and hope to have an agreement in the next 24 to 48 hours, according to the Tampa Bay Times.
Kelly has been the Ducks' coach for three years, reaching three consecutive BCS games while winning the conference title in all three seasons. Last month, Kelly led the Ducks to their first Rose Bowl victory in 95 years, beating Wisconsin, 45-38.
Kelly also coached current Bucs running back LeGarrette Blount when he played at Oregon. Kelly suspended Blount for eight games in 2009 after the running back punched a Boise State player following a season-opening loss.