Wilshere, whose current deal at the Emirates Stadium expires on July 1, is yet to agree fresh terms with his boyhood club after forcing his way back into the team last season.
The 26-year-old struggled with injuries in recent seasons, but made 38 appearances last term in Arsene Wenger's final campaign at the helm.
According to Sky Sports News, Wilshere's future remains uncertain but both parties are allegedly keen to thrash out an agreement in the coming days.
The source adds that a loyalty payment due for the midfielder is complicating the Englishman's potential departure from the club.
Wilshere has been with Arsenal since the age of nine and has made 125 appearances for the team.