Wilshere has been restricted to Europa League and domestic cup opportunities so far this season, but has impressed in his limited appearances.
The 25 year-old has entered the final year of his £90,000-a-week contract and will leave the Emirates for free next summer should Arsenal not renew his deal.
Bleacher Report claim Fenerbahce will attempt to lure the England international to Turkey following the recent injury to midfielder Mehmet Ekiri.
Wilshere has been part of the furniture at Arsenal since he was 11 years-old. Injuries have blighted the playmaker’s career, but after recovering from a broken leg last season, the England man is enjoying his football.
With just 65 minutes of Premier League action under his belt, it would be understandable if the midfielder chose to take up the option of leaving for regular football.
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