Wilshere is currently on loan at Bournemouth after moving to the south coast in the summer transfer window.
He has impressed for the Cherries, who are currently 8th in the Premier League table, and it is unknown whether he has a long-term future at the Emirates.
He currently has just 18 months remaining on his current deal and so far there have been no suggestions that a new deal will be offered.
The Gunners are well stocked when it comes to central midfielders, hence why he left to get regular football with Eddie Howe’s team.
At this moment in time a departure looks likely and according to the Mirror, Goodison Park could be his next destination.
The newspaper reports that Ronald Koeman is a long-term admirer of the midfielder.
The Dutchman is reportedly on the hunt for a creative midfielder and the Arsenal and England man fits that bill.
They could face competition for his signature, though, with Manchester City also said to be keeping track of his situation.