The England and Gunners midfielder has struggled with groin and hamstring injuries this season, but is in line to make a comeback for the May 30 showdown with Aston Villa.
Oxlade-Chamberlain has not played since the March 9 FA Cup win at Manchester United.
However, the Telegraph claim the 21-year-old is now back in training and ready to stake a claim for a spot in Arsene Wenger's squad.
The Arsenal boss revealed Oxlade-Chamberlain will not feature against Swansea on Monday, as he slowly builds up his fitness ahead of a return to action.
"Chamberlain is not available, Arteta will be short so it will basically be a similar squad [to the one that faced Hull]," Wenger said.
Mathieu Debuchy is also out, while Danny Welbeck and Aaron Ramsey are doubts for the visit of Garry Monk's side.