It was thought he would be out for at least a fortnight but he is now in line to appear at Highbury.
"Kevin has been going through some rehab work with our physios," manager Sam Allardyce revealed from the United Arab Emirates.
"He's been in the sea and everyone knows that the salt in the water can aid your recovery.
"Hopefully he will be fit for Saturday. He is in with a chance."
The squad are heading straight to London on Friday from Dubai, where they have been enjoying good facilities as well as good weather.
"We have been using two very good pitches," said Allardyce.
"We have also played a bit of tennis and golf and gone swimming. It has been a really good period for the players to recharge their batteries after putting so much effort into recent games."
Meanwhile, Abdoulaye Faye is set to return also, after returning from the African Cup of Nations.
"I hope he is champing at the bit and raring to go," said Allardyce.
"Firstly because of how he played against them last time and, secondly, because of his frustration at not playing as much in the African Nations Cup as he would have wanted.
"I hope that that gives him the edge on Saturday and he can hit the form immediately that he was showing when he left us.
"We have missed that while he has been away.
"That is the gamble I have to take with my African Nations Cup players in this game.
"I have to decide if they are going to peak for me immediately.
"That's the risk I may have to take. If I do, I hope it has a positive outcome."