The 25-year-old, currently halfway through a season-long loan spell at Bournemouth, has yet to be offered a new contract at Arsenal with his current deal set to expire in summer 2018, and is now contemplating his next move in his career.
Arsene Wenger has stated previously that he will offer Wilshere a new deal to remain at Arsenal, but the England international will need assurance of regular first-team football before signing on the dotted line.
Manchester City, Everton and AC Milan, who were reportedly keen to sign him on loan last summer before joining Bournemouth, are now all believed to be monitoring his situation at the Emirates.
Wilshere has been in fine form for Bournemouth this season appearing regularly under Eddie Howe. He has made 15 appearances (13 starts) so far this season for the Cherries.