Jack Wilshere could stay at Bournemouth beyond the end of the season, according to the club's chairman Jeff Mostyn.
Wilshere arrived last month on a season-long loan from Arsenal after Arsene Wenger could not guarantee him regular first-team football.
Wenger said this month he still wants the "world-class" England midfielder to see out his career in north London, but in the meantime, Wilshere has settled quickly at Bournemouth.
Eddie Howe expects him to have "a massive impact" on Bournemouth's season, while Wilshere tweeted after Saturday's defeat of Everton that he was "proud to be part of this team".
And Mostyn, quoted in the Evening Standard, said: "I think anything is possible. The best we can do is integrate Jack into the team and help him fulfil what he wants.
"Whether or not we will go beyond a season, I think everything is possible.
"You have to be realistic and Jack may well consider his home to be back at Arsenal. If that was the case then we couldn't disagree with his decision - and the decision will be his.
"But if there is a possibility and Eddie Howe decides that he's somebody he wants to keep, it will be up to him.
"He will have to persuade [owner] Maxim Demin to unload a huge treasure chest in order to keep him. That would be the $64m question - it may even be the £64m transfer fee!"