The R's are in hot pursuit of the 22-year old France international and Redknapp wants a potential deal to be finalised as soon as possible before anyone else comes in for his services.
"We are working on it, that's all I can say," he said.
"But you have to move quickly. The longer it goes on, the more people see his name in the papers."
To add some fuel to the fire, Rennes boss Pierre Dreossi suggested the M'Vila may have already played his last game for the club but did not reveal the players destination.