The Chilean international picked up a hamstring strain in the 1-1 draw at Norwich City, and an initial prognosis suggested he would be out for up to four weeks.
However, Sanchez has started running again following his time with the Chile national team physio back in his homeland and is due to return to London on Sunday ahead of Monday’s training session.
“He trains with us on Monday morning. I sent him back to Chile, where he has been with the physio of the national team, and we will see what kind of state he is in next week,” Wenger said.
On the prospect of being available to face Manchester City, the Frenchman added: “He may be a bit short for City, certainly, but with Alexis you never know.”
Sanchez has been a key performer for Arsenal so far this season, scoring six goals and adding one assist in 13 Premier League matches, including a hat-trick at Leicester City.
The former Barcelona star’s injury coincided with setbacks for Francis Coquelin and Santi Cazorla, leaving the Gunners extremely short of options in key areas.
However, Wenger’s side have performed admirably without the trio, first beating Sunderland 3-1 before progressing to the Champions League knockout stages with a 3-0 win at Olympiakos.
Arsenal face Manchester City four days before Christmas, giving Sanchez just under 10 days to recover.
It may come as one game too soon, and the worst possible scenario would be aggravating his hamstring further in a bid to bring him back, despite the importance of the encounter.
Following the festive period, Wenger has a big decisions on his hands in regards to possibly handing Sanchez a winter break following two years of non-stop football