Northerners Lille, who take on Lorient on Sunday, were 15th in the standings after seven rounds of matches but with eight games to play they trail fourth-placed Saint-Etienne, who occupy the Europa League qualifying spot, by one point.
Lille have 49 points and second-placed Olympique Marseille, whom they entertain in the following round of matches, occupy the Champions League qualifying berth five points ahead of them, with third-placed Olympique Lyon on 53.
"We've been maintaining the gap with OM. What is interesting is that we're one point behind the fourth-placed team," coach Rudi Garcia told the club's website.
"We now need to make the most of our two home games against Lorient and Marseille. The idea is to take part in the final sprint."
"My goal is to be back in two or three weeks," Mavuba told the club's website.
Leaders Paris Saint-Germain, who sit on a seven-point cushion, travel to mid-table Stade Rennes on Saturday for a game sandwiched in-between Tuesday's 2-2 draw in their Champions League quarter-final first leg against Barcelona and next Wednesday's return leg at the Nou Camp.
Lyon, who slipped down to third after back-to-back defeats against Bastia and Sochaux, travel to strugglers Stade Reims on Sunday while Marseille take on Girondins Bordeaux in Friday's curtain raiser.
OM are sweating on centre-back Nicolas N'Koulou's fitness after the Cameroon international sustained a thigh injury in last weekend's 1-0 win at Nice.
"It's getting better and better. I felt a sharp pain and I did not want to force it. I'm treating it and I hope I will be available for the game," he told the club's website.
