The report, citing an NFL source, said that Culpepper is expected to sign the contract Monday.
Culpepper has played nine seasons in the NFL with the Vikings, Dolphins and Raiders. He has thrown 142 career touchdown passes in 92 games.
Culpepper burst onto the scene as a member of the 2000 Vikings, throwing for 33 touchdowns in the regular season. Minnesota finished 11-5 and made the NFC Championship game that season, but Culpepper hasn't had a winning record in any individual season since.
The Lions, though, appear willing to take a chance on Culpepper. Their current starter — Dan Orlovsky — has had his share of issues, throwing for just three touchdowns in six games and providing one of the season's blooper highlights when he took a safety in an Oct. 12 game at Minnesota by running out of the end zone while dropping back to pass.
Detroit is 0-7 and four games out of first place in the NFC North.