Arsenal chairman Peter Hill-Wood has admitted the club could lose Robin van Persie if the striker demands excessive wages.
Van Persie, 28, held talks with Arsenal over his future at the end of the 2011-12 season, with his current contract expiring in the summer of 2013.
No resolution was struck during the discussions, meaning clarity over whether the Dutchman will commit to a new deal is uncertain until at least the conclusion of Euro 2012.
Clubs including Manchester City have been linked with Van Persie, although on Saturday the forward's father played down the speculation.
Hill-Wood said in the Sunday Mirror: "He is vital to us and has been an extremely good captain. But if somebody comes along and offers Robin £250,000 a week then I am afraid we cannot compete with that.
"With players, you never know what they are going to do. Some players say they want silverware but when they have the chance to earn extraordinary money that has been pumped into the game, then you just have to hope they will stay because they are happy and loyal where they are.
"There are players like Ryan Giggs and Paul Scholes at Manchester United who have been loyal to one club, but players like that are few and far between.
"Hopefully we can reach agreement with Robin and ideally he will extend his contract. We have already brought in one new player in Lukas Podolski and I believe we will bring in more. I am confident we will, in fact.
"I just hope that Robin will be with us next season because I genuinely feel we can make a real challenge for the Premier League title. We had an atrocious start to last season but we recovered to finish third, which was a marvellous achievement when you look at the problems that we had with injuries."