England coach Gareth Southgate refused to consider Wilshere for his squad this week due to a lack of regular football he's seen this season.
The Mirror says if there seems no way back for him at the Emirates, a clutch of clubs could look to see if they can tempt him to leave in the January window with the prospect of more games.
West Ham, Swansea and Spanish side Real Betis are all watching developments and could be ready to make a move, given any encouragement.
Wilshere stated: "He said I need more football. That is what I have got to do.
"I have got to take it on board, try to get into the Arsenal first team and hopefully I'll be selected. I have just come back to full fitness. I am happy with where I am, playing-wise. I am trying to get into the Premier League team.
"At the moment I am concentrating on the now. The future will take care of itself. All I have got to do is stay fit and play my football. I want to stay at this club — I have said that many times."