Wilshere has been missing since suffering a hairline fracture to his foot in England's friendly win over Denmark on March 5.
Oxlade-Chamberlain is struggling with a groin problem and left-back Gibbs has experienced ankle trouble.
Wenger provided an update on the trio on Thursday, three days before the Premier League meeting against West Brom in which Arsenal could secure a top-four finish and a place in the final UEFA Champions League qualifying round.
"Gibbs will be a bit short for Sunday," Wenger told his club's official website. "The good news is that he's back in fitness training but he is not back in the full training group yet.
"They (Wilshere and Oxlade-Chamberlain) are not ready yet.
"Alex is in treatment at the moment and not in training. It's very difficult to give you a timescale on him at the moment."
