The Gunners midfielder has less than three months remaining on his current deal and has been delaying signing fresh terms at the Emirates Stadium.
Reports suggest Wilshere has been offered a lower basic salary to remain at Arsenal, with talks seemingly at an impasse despite the contract being on the table for some time.
Having struggled for fitness during the past three years, culminating in spending last season on loan at Bournemouth, the 26-year-old has firmly re-established himself in Wenger's side in recent months.
That led to an England recall and, although Wilshere was forced to withdraw from the squad for the March friendlies against Holland and Italy with a minor knee injury, Wenger believes the player's future will be sorted soon.
"I cannot give you any news because I don't really know what is in his mind," the Frenchman said when asked for an update on Wilshere's contract wrangle.
"He has an offer that is on a long-term contract basically, and I hope that at some stage he will sign it.
"I think he will make his decision before the end of the season. he will not want to go to the World Cup and not have settled his situation because that would not be reasonable as well I think.
"He has the freedom to make that decision, he knows I want him to stay."
Mesut Ozil was in a similar position to Wilshere earlier in the year but signed a vastly-improved deal to end speculation over his own future.
However, with Wilshere's negotiations taking longer, Wenger insists players cannot simply be paid what they ask for.
"If you think like that, there's no limitations anywhere," he said.
"As a club. you want the players to stay and to be paid well, and I believe that everybody would agree that we pay our players very well."