The 65-year-old Hoops boss remains wary of getting involved in a bidding war for the France international's signature as he seeks to add to his squad during the January window
The 22-year-old France international has attracted interest from the likes of Arsenal and Tottenham in the past after carving out a burgeoning reputation for himself back in his homeland, but a series of incidents off the pitch have seen plenty of big clubs withdraw from chasing his signature.
As Goal.com exclusively revealed on Friday, Spurs have rejoined the race for M'Vila and it remains unclear whether Redknapp's side are still the favourites to sign him, with the manager guarded in responding to questions of reported interest in the player from Everton and an unnamed Russian club.
"We're still working on it, you need to get deals done quickly. The longer it drags on the more people get involved, he’s good value," Redknapp told reporters.
After taking the lead through a first half goal from Loic Remy on his debut for the club, Joe Cole's equaliser in the second half ensured that honours remained even at Upton Park, with Redknapp revealing that his side came close to signing the playmaker from Liverpool earlier in the window.
He added: "I wanted Joe and I think we could have had Joe. We were talking to him three weeks before West Ham even came on the scene but it just went on too long.
"Once West Ham came in for him he was only ever going to go there, this is his club but the deal just dragged on too long.
"Sometimes with deals you have to get them done quickly and once others get alerted it can change. He had some bits and pieces to sort at Liverpool which held it up."
Sam Allardyce believes Redknapp has made QPR more difficult to beat since taking charge, drawing favourable comparisons to the side West Ham beat 2-1 at Loftus Road back in October under predecessor Mark Hughes.
"They are [more difficult to beat], they're not as open now and they're not playing the attacking football that Mark Hughes tried to get them to play," Allardyce stated.
"Now they make life extremely difficult for you to break them down, but we couldn't find a way to put the ball into the back of the net more. They're going a long time without losing too many games.
"Ultimately in the end [Redknapp] knows he's going to have to start winning more games and it frustrated us, just as it did with Chelsea and Tottenham. They've got a system that works for them, when you play with the tactics of QPR there's not a lot of space to break them down."