The Gunners midfielder is facing an uncertain future at the north London club having failed to agree a new deal.
Wilshere is set to become a free agent at the end of the season unless the Gunners can tie down the midfielder to a new contract.
The 26-year-old has been linked with a potential switch to Chelsea FC and Liverpool FC at the end of the current campaign.
The Arsenal star has scored one goal and has made two assists In 19 games in the Premier League after fighting his way back into first-team contention.
Former Arsenal star Groves is confident that Wilshere will remain at the north London club despite continued uncertainty surrounding his future.
“I think Jack Wilshere will definitely stay at Arsenal this summer,” Groves told sportingbet.
“The hierarchy is trying to cut his wages but they should put him on a pay-as-you-play deal now that he’s got over his injuries and he’s getting back to his best.
“There’s not many players who have the vision he has and everything he does is about moving forwards.
“Jack Wilshere would be a big miss because his soul is at the club and the fans love him.”
Arsenal finished fifth place in the Premier League table last term to miss out on a spot in the Champions League for the first time under Arsene Wenger.
England international Wilshere has endured an injury-hit Arsenal career so far despite his undoubted talent since breaking into the Gunners team.
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