Wilshere has made five starts for the Gunners in the early stages of the 2017-18 campaign, but all of those have come in the cup competitions.
Indeed, the 25-year-old, who spent last season on loan at Bournemouth, has only played 25 minutes of Premier League football this term.
Wilshere impressed off the bench against Manchester City on Sunday afternoon, however, and Keown has insisted that the Englishman deserves a recall to Wenger's Premier League team.
"This defeat proved that it is time for Jack Wilshere to return to Arsenal's first team," Keown wrote in his column for the Daily Mail. "Arsene Wenger's game plan was to stop Manchester City playing and for periods, it worked. But where was Arsenal's midfield creativity?
"They were not able to play the way they wanted in the final third and that is where Wilshere would have made a difference. He commits defenders, he creates space, he finds that pass for Alexis Sanchez or Alexandre Lacazette.
"Sanchez and Mesut Ozil did not have good games. If they are not going to sign contracts, then Arsenal have to start looking to the future. Does Wenger play Wilshere instead of Ozil, or in midfield in place of Granit Xhaka?"
Wilshere's current contract with Arsenal will expire at the end of the season.