The 30-year-old reigning Football Writers' Association Footballer of the Year has been linked with a host of Premier League clubs following the Hammers' relegation to the Championship.
Parker has admitted he would like to remain in the top flight in order to keep alive his England career, leading to reports linking him to the likes of Arsenal, Aston Villa, Tottenham and Chelsea.
The latter have been hit this week by the news Michael Essien will be out for the next six months and reports have suggested they are considering a loan move for the West Ham midfielder.
Parker, who played for the Blues between 2004 and 2005, has reportedly been lined up as the Ghanaian's replacement and, while Sullivan insists there has been no contact, he says a loan deal would suit the Hammers.
"We have had no approaches from any club officially," he told Sky Sports News.
"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."