West Ham could lose Dimitri Payet to Barcelona or Real Madrid, according to Hammers co-owner David Gold.
The France international, 29, is shining at Euro 2016 after an impressive debut campaign in the Premier League following his move from Marseille, which was reported to be worth £10.7million.
Gold insisted West Ham are desperate to keep Payet, but acknowledged that Barca or Madrid could be too difficult to fend off if his player wanted to join them.
"We will fight tooth and nail to make sure Dimitri pulls on a claret and blue shirt next season," Gold said to The Sun.
"We want to improve our squad and Dimitri is an integral part of what we are trying to do.
"But we also must be realistic. If Barcelona or Real Madrid made a bid and he wanted to move there, it would be difficult to keep him.
"You can't have a great player like Dimitri and expect no-one to make a bid, especially with the performances he is producing at the Euros.
"The phone has not rung yet, although we know there is a chance it will once the tournament is over. We are not silly. Yet, let me be very clear, we would not welcome a call."
Gold stressed West Ham are under no financial pressure to sell Payet and does not want them to be perceived as a selling club - even though any departure of the playmaker, under contract until 2021, would secure a massive profit.
He continued: "The club certainly doesn't need to sell him so this is not a case of, 'We have bought him for £10m and can now make a tidy profit'."
The co-owner also discussed the challenge of taking on England's biggest clubs in the transfer market after Michy Batshuayi - who they had targeted - seemingly opted to join Chelsea, with a EUR40m move believed to be close to completion.
"We are desperate to bring in quality players. Nowadays we are competing with Chelsea, Arsenal, Manchester United or Manchester City. For them, resources are virtually unlimited," he said.
"But in the real world at West Ham, you have got two English owners who pay their taxes, without the resources of those other clubs.
"We are not a club yet that can compete on that scale with them, but we are no longer a selling club - we are a spending club and investing in our future.
"The gap is shrinking between us and them. Big fish eat little fish. West Ham have been a little fish for too long and the only way to stop being eaten is to become a big fish."