But West Ham would consider loaning the England international out for the season.
The 30-year-old reigning Football Writers' Association Footballer of the Year has been linked with a shot of Barclays Premier League clubs following the Hammers' relegation to the npower Championship.
David Sullivan: "We have had no approaches from any club officially.
"We keep hearing rumours and I would be wrong to comment further.
"I have not spoken to Scott myself. I think he has indicated and his agent has told me for his England career that he would like to play in the Premier League.
"But if we can't get the right fee for him I think he accepts he will be playing for West Ham next year in the Championship.
"He is a supreme professional and I am sure he will do a wonderful job whether he is with West Ham or somebody else.
"I mean we would love a deal - and this has been mooted - that maybe we loan him out for the season for a substantial fee and then when we get promotion he comes back to us.
"That sort of deal would appeal to us because we love Scott.
"We would obviously want a loan fee because he has substantial value and has three or four years left of his career.
"They would probably be getting the best of those three of four years.
"He is at the absolute peak of his game at the moment and is playing out of his skin.
"He would be a superstar wherever he goes and in the Championship he would be the best player."