The England international picked up a hamstring injury in his side's 2-0 win over Southampton on 10 May, forcing him to miss the north London club's last three league wins as they finished the season fifth in the table.
According to the Evening Standard, Arsenal believe that the 23-year-old will be fit in time for the final on Saturday. Arsene Wenger shifted to back three and Oxlade-Chamberlain has excelled in the right wing-back role since then.
The Frenchman earlier confirmed that the initial diagnosis revealed Oxlade-Chamberlain's injury was not as bad as first feared. In his absence, the Arsenal manager has fielded Hector Bellerin in that role and the Spain international has excelled in that position.
In the last three matches, Bellerin has scored a goal and registered two assists. Should Oxlade-Chamberlain fail to recover in time, Wenger is likely to continue with Bellerin in the right wing-back position.
Arsenal registered a 3-1 victory over Everton in their last league fixture of the season at the Emirates. Laurent Koscielny was shown a straight red for his late tackle on Everton forward Enner Valencia, while Gabriel Paulista was forced off the pitch with a stretcher. There are fears that the Brazilian has suffered a knee ligament damage and will undergo scans to find the full extent of the injury.
The France international centre-back is suspended for the final, while Gabriel is unlikely to be fit to face the Premier League winners. The clash against the Merseyside club also saw Alexis Sanchez replaced in the second half as a precaution due to a hamstring injury raising a few concerns over his involvement in the FA Cup final.
The same report claims that there are no major concerns over the Chilean international's involvement to face Antonio Conte's side this weekend. With Koscielny and Gabriel set to miss the cup final, Wenger is left with Rob Holding, Per Mertesacker and Shkodran Mustafi as the other centre-backs in the squad.
Mustafi suffered a blow to his head in Arsenal's 2-0 win over Sunderland. Despite that, the German international completed a full match. He later fell ill and missed his side's clash against Everton. The defender is being monitored after showing signs of concussion, reports the Telegraph.
Arsenal are optimistic that the defender will be fit in time for the Chelsea clash. The Evening Standard report also confirms that Kieran Gibbs could return to the starting lineup after a thigh injury forced him to sit out against Everton. With Gibbs returning to the starting lineup, Nacho Monrela and Holding will start in the three-man defence.