Wilshere, whose current Arsenal contract will expire next summer, spent last season on loan at Bournemouth after being deemed surplus to requirements by Gunners head coach Arsene Wenger.
The 25-year-old is still recovering from the broken leg that he suffered while on loan at Bournemouth in April.
As a result, the midfielder did not travel with the Arsenal squad on their pre-season tour of Australia and China as he stayed at the club's training ground to continue his rehabilitation.
It is widely thought that Wilshere's Arsenal career is over, and according to The Sun, Newcastle lead a list of interested clubs which also includes West Ham United, Crystal Palace and Bournemouth.
Wilshere came through the youth system at Arsenal, and has made 159 appearances for the Gunners since debuting during the 2008-09 campaign.