Wilshere has not featured for Arsenal since late November due to an ankle injury while Oxlade-Chamberlain has been out for a month following a groin problem.
However, both could play a part for Wenger at Selhurst Park as Arsenal look to put the pressure on fourth-place Southampton, who play Liverpool on Sunday.
Wenger's men have won their last four meetings with Palace although this weekend the Frenchman will be without Aaron Ramsey (hamstring), Mikel Arteta (ankle) and Mathieu Debuchy (shoulder).
"Jack is fine. [Oxlade-Chamberlain] is close, he will join in normal training," Wenger told the club's official website.
"Ramsey is still out. The two other injuries are Arteta and Debuchy. Apart from that we have some uncertainties about [Mathieu] Flamini and [Hector] Bellerin - they are doubtful for Saturday. Everybody else is OK.
"Bellerin is his ankle and Flamini has a tight hamstring. We’ll see. We'll have tests [on Friday]."
Wenger's side have taken 12 points from their last possible 15, with a north London derby defeat their only real low point of recent weeks - form that has partly led Alan Pardew to describe the clash as a "bonus game" for his Palace side.
With Yannick Bolasie and Mile Jedinak only recently back from international competitions - the latter a doubt for this weekend due to an ankle knock - and Yaya Sanogo ineligible against his parent club, Pardew feels a draw would represent a major result for his side.
"I've had to be patient a little bit because Bolasie, Mile, [Marouane] Chamakh's had injuries and Yaya will obviously miss this game," he told reporters.
"We've not actually got it all together and I don't think this weekend we will.
"We're not quite there but by the time we get to West Ham, Southampton, we're going to be pretty close hopefully.
"So, this for us in a way is a bonus game, because no-one will expect us to get anything really.
"If we can get a point, or three points, it would be a massive boost for us."
James McArthur (thigh) and Jonathan Williams (groin) are also likely absentees as Palace look to pull further clear of danger, having obtained 10 points from a possible 15 since Pardew's arrival from Newcastle United.
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