Wesolowski suffered a slight tear to his medial ligament during the closing stages of Tuesday night's 2-0 defeat at Preston and missed the 1-0 win at Bury on Saturday.
The 25-year-old midfielder is set to have an injection which will determine whether or not he is able to play a further part in Oldham's battle against relegation from npower League One.
"We will have to see how he comes through the injection - he could dramatically improve or it could make no difference," Latics boss Lee Johnson told the club's official website.
"James won't be ready for Tuesday (at home to Yeovil), but possibly could be for Saturday (when Crawley visit Boundary Park) or he could be out for the season. We will have to see how it settles."
Oldham are currently one place and two points above the relegation zone.
- Sports & Recreation