The newspaper said the Bucks signed Jennings to a three-year, $24 million contract and then sent him to the Pistons for Knight, small forward Khris Middleton and forward Slava Kravtsov.
The reported move came shortly after Milwaukee announced the signing of free agent guard Gary Neal to a reported two-year contract worth $6.5 million.
Jennings, 23, had a breakout season in 2012-13, averaging 17.5 points, 6.5 assists and 3.1 rebounds over 80 games for Milwaukee, which took him as a 10th-overall draft pick in 2009.
In Detroit he joins ex-Atlanta Hawks forward Josh Smith, who signed a four-year, $56 million deal with the Pistons this month.
Knight, tabbed by the Pistons with the eighth-overall selection in 2011, averaged 13.3 points last season, while Middleton posted 6.1 points per game in 27 contests.