The 25-year-old was linked with a move away from the Emirates in the summer after his loan spell at Bournemouth came to an end.
The midfielder has struggled with injury problems over the last few years and was forced to miss pre-season as he recovered from a broken leg.
Wilshere, who has been part of the Arsenal fold since 2001, has made three appearances for Arsene Wenger so far this season, none of which has been in the Premier League.
According to The Times, the midfielder is now seriously considering leaving the Emirates in three months' time in order to boost his chances of earning a place in England's squad for the Russia World Cup next year.
The report claims that 22 clubs expressed an interest in Wilshere during the summer, and if he makes it clear that he intends to make a change, those outfits could return.
The 34-capped England international has not represented his country in over a year.