The team says the move is expected to become official next week.
Best's agent did not immediately return an email seeking comment.
Best also missed time during this preseason because of a concussion, and when he was a college player at California, he missed a few games after a fall knocked him out and sent him to the hospital with a concussion and sore back.
The Lions drafted Best in the first round in 2010. He ran for 555 yards as a rookie last season and caught 58 passes despite toe problems.
He started the first six games of this season, running for 390 yards on 84 carries. Schwartz said he started experiencing "concussion-like symptoms" after the loss to San Francisco.
Detroit has been unable to keep anyone in their backfield healthy. In addition to Best's injury problems, Jerome Harrison had surgery last month for a brain tumor. Rookie Mikel Leshoure tore his left Achilles' tendon before the season even started.
Kevin Smith gave Detroit a boost, running for 140 yards last weekend in a win over Carolina, but Smith went down with a right ankle injury in Thursday's 27-15 loss to Green Bay.
Smith recovered from knee and thumb injuries the last two seasons, and he returned to the Lions earlier this month after being out of football.
The Associated Press contributed to this report.