Redknapp is keen to strengthen his squad during the January transfer window and has already seen Loic Remy added to his ranks in an £8million move from Marseille.
Speaking on Tuesday night, the Loftus Road boss said he hoped the arrival of M'Vila would be wrapped up in the coming days, but the move is yet to be finalised.
And now the former Tottenham boss has admitted that while discussions are on-going between all parties, there is a concern that rival bidders could hijack their swoop, with Everton and Tottenham also reported to be interested in the 22-year-old France international.
Redknapp told reporters after Saturday's 1-1 draw with West Ham, when Remy opened his account for the Rs: "We are working on it, that's all I can say.
"But you have to move quickly. The longer it goes on, the more people see his name in the papers."