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The 26-year-old will be a free agent at the end of the season and is yet to discuss terms about extending his stay at the Emirates.
He spent last season on loan at Bournemouth and was told he could leave in the summer but Wilshere was determined to stay and fight for his place.
The England international has been plagued by injuries throughout his career and struggled to force his way into Arsene Wenger’s plans during the first half of the season.
But he has recently enjoyed a spell in the side, starting the last six Premier League games, and scored the opener in last week’s draw with Chelsea.
Jack Wilshere next club odds

“Arsenal are keen to lower his weekly salary and introduce bonuses for playing games, meaning he could actually earn more if he plays regularly.”
And according to the Mirror, the Gunners are set to negotiate a new contract - although Wilshere may have to accept a pay cut.
He currently earns £90,000-a-week, which increases to £120,000 with bonuses, but there are concerns about his fitness.
Arsenal are keen to lower his weekly salary and introduce bonuses for playing games, meaning he could actually earn more if he plays regularly.
Wilshere has been linked with a move away this month in order to seek regular game time ahead of this summer’s World Cup.
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But his recent run in the team may have convinced him that he has a future at the club.
Arsenal are currently sixth in the Premier League, eight points behind second-placed Manchester United.
They’re back in action on Wednesday as they visit Chelsea in the first leg of the Carabao Cup semi final.