Wilshere, who has struggled in recent seasons with multiple injuries, is thought to not have made up his mind on whether to stay at the Emirates or seek a new opportunity elsewhere.
The England international, who was left out of Gareth Southgate's World Cup squad, is unsure whether he will get sufficient playing time under new Arsenal manager Unai Emery, or whether a move away from his boyhood club would be more beneficial for his career.
The players deal will run out on 1st July, and it is unsure as to how regularly he will play with his current team trying to sign Uruguyan midfielder Lucas Torreriera from Sampdoria in the Serie A.
According to various newspaper reports, several teams in both the Premier League and Italy's Serie A would be interested in signing the 26 year-old on a free transfer.