Mays (wrist) is targeting a Week 7 return from injured reserve, Dave Birkett of the Detroit Free Press reports.
McMillan has been diagnosed with a PCL sprain in his left knee, Jenna Laine of ESPN.com reports.
Gainwell turned three carries into minus-four yards and added two catches on five targets for 14 yards in Sunday's 23-16 loss to the Vikings. He also returned six kickoffs for 160 yards and added a tackle.
McMillan aggravated the left knee injury he dealt with during training camp, Jenna Laine of ESPN.com reports.
Buccaneers head coach Todd Bowles said Monday that Mayfield (thumb) is expected to miss three weeks, Adam Schefter of ESPN reports.
Head coach Todd Bowles said that Irving won't be included on the Buccaneers' Week 4 injury report, despite missing the final two possessions of Sunday's 23-16 loss to the Vikings, Scott Smith of the team's official site reports.
Head coach Todd Bowles said Monday that Daniels will step in as the Buccaneers' new starting quarterback while Baker Mayfield is out for a "minimum of three weeks" due to a dislocated right thumb, Cameron Wolfe of NFL Network reports.
Mayfield underwent an MRI on his dislocated right thumb Monday that revealed no fracture, tendon or ligament damage, but the quarterback is still expected to miss time, Jeremy Fowler of ESPN.com reports.
McMillan is slated to undergo an MRI on his left knee Monday, Jenna Laine of ESPN.com reports.