Redknapp and chief scout Ian Broomfield made the trip following QPR's goalless draw with the manager's former club Tottenham at Loftus Road on Saturday lunch-time.
Defensive midfielder M'Vila is thought to be high on Redknapp's list of transfer targets this month as he looks to bolster his struggling squad, with the Hoops rock-bottom of the Premier League.
He was a fan of the France international while in charge at Spurs but failed to bring him to White Hart Lane and has previously admitted he is unsure whether the 22-year-old wants to join QPR.
Rangers are rumoured to have offered €9million (£7.4m) as Rennes hold out for €12m (£9.9m).
Redknapp could face competition for M'Vila's signature, with Fulham understood to have shown a late interest, while the midfielder has also been linked with a Russian move.