Wilshere, who spent last season on loan at Bournemouth, is into the final year of his current deal with the Gunners and has been linked with Newcastle United and Aston Villa.
The 25-year-old is closing in on a return to full fitness after recovering from his latest injury setback and Wenger stated that he has no doubt about Wilshere’s quality.
As reported by the Press Association, Wenger said: “If he gets back to his best and wants to stay, we have to sit down, I think, later in the season. I don’t rule that out.
“You know how much I love Jack and his talent, I started him at the age of 17 but today in the football world you need to be a consistent presence and what is at stake for Jack is not his quality, his talent or his determination, it is whether he is a consistent presence at the top.
“I hope he can manage to do that and after nobody questions his quality.”
Jack Wilshere attempted 1,008 passes in the Premier League last season.
However, Wenger refused to rule out the possibility that Wilshere could leave Arsenal before the transfer window closes next week.
He said: “I’m open, you know, with Jack.
“We have honest conversations. I’m open to what is the best for him.
“He is at the stage of his career where he needs to play and I can guarantee him today that, and I think I’m quite open on that.”
Despite the many frustrations he has endured with injuries, Wilshere remains a very talented player and impressed in patches for Bournemouth last season.
In the Premier League last season, Wilshere was successful with 84 per cent of the passes that he attempted, while he created 34 chances for his team-mates.