The Spain international has been out since late October, having made just 11 appearances in all competitions this season.
But Cazorla, 32, is set for an even longer stint out, with Wenger only hopeful over his availability late in the season.
"He's far from starting to run again," Wenger said.
"He had a little procedure, yes, but we have a meeting with the medical people to see what it was.
"Yeah, I hope so [that he'll be available for the run-in].
"Because once you start to go out [running outside] you have to count six weeks' preparation. At the moment he's not at that level, so let's hope he can come back in the next three or four weeks on the pitch."
Arsenal is fifth in the Premier League table ahead of a trip to struggler Swansea City on Sunday (AEDT).