The Sun reported that the midfielder rejected a new contract in the summer and plans to quit Arsenal at the end of the season.
Gunners boss Arsene Wenger claimed this week that there had been no fresh talks with the 25-year-old midfielder.
Yet Emirates chiefs wanted Wilshere to sign a new deal during the summer but were knocked back.
A source close to Wilshere said: “Arsenal didn’t want to loan him out again unless he signed a new contract — but he didn’t want to sign one.
“If Jack gets back into the Arsenal team on a regular basis and feels he is seriously part of the club’s plans, there is still a chance he might stay.
“However, as things stand, he is still of the view that he will be leaving at the end of the season.
“But he will be giving it his all for the club and will remain professional.”