The Chilean forward will not be ready for the clash with Liverpool, but could make the game with Stoke.
The Chilean forward has been out injured since November after picking up a hamstring injury in the draw with Norwich City.
He had hoped to return in the middle of December, but then suffered a setback that has ruled him out until now.
There had been suggestions that he would be fit for the big game at Anfield, but Wenger has now ruled him out of the trip to Merseyside.
It is not all bad news however; as Wenger suggested that the star forward may be back for this weekend’s trip to Stoke instead.
“With Sanchez I think the Liverpool game will come too soon for him,” he told his pre-match press conference.
“There is a chance for Sunday and overall the situation is getting better.”
“If you listen to Alexis he can always play, even when he is injured. We try to be cautious, it is a muscle injury and you never know. He is very close.”
Similarly, the club will have to conduct late tests on backup goalkeeper David Ospina before the game.
The Colombian missed the 3-1 win over Sunderland in the FA Cup on Saturday, with Petr Cech having to start in his absence.
He will now be handed a late fitness test before the game with Jurgen Klopp’s side, while duo Mesut Ozil and Mathieu Flamini will also return to the side.
“Look, we should have Ozil and Flamini available. We have to test Ospina, who was not available on Saturday,” added Wenger.