The 27-year-old is expected to leave Old Trafford this summer having handed in a transfer request at the end of the season, and has attracted interest from both the Blues and Arsenal.
Chelsea have seen two bids rejected for the striker, but Redknapp feels that the saga has already gone on for too long and is in danger of threatening United's season.
"Wayne Rooney needs to leave Manchester United," Redknapp told the Daily Mail. "It's the best thing for him but, by making Chelsea wait, United are casting a shadow across their own season. The modern game and its ways make it very difficult to keep unhappy players.
"David Moyes doesn't seem to want to be the manager who sells the best player of his generation twice (he sold him as Everton manager), so Rooney may have to force the move by asking for a transfer. There is always a way back but the best thing for him is to play for Jose Mourinho.
"Right now, he is injured for his club but will play for his country this week. It can't go on and, with two years left on his contract, this is the best chance to cash in. I expect the deal to happen before the deadline - 11pm on September 2."
Rooney joined Manchester United from Everton in 2004.