Having already been sacked by owners that did not employ him twice, Allardyce expressed his surprise at the news, but Sullivan says he has nothing to worry about.
He told The Sun: "The whole thing is nonsense. I can assure Sam he has an unbreakable two-year contract and he is the perfect man for the job.
"I can only think the motivation for this 'takeover' bid is PR. If there was a genuine Russian billionaire out there willing to pump hundreds of billions of pounds into West Ham then we'd step aside for the good of the club.
"But when someone offers to buy your club for buttons and does it via Twitter it is most unhelpful at a time when we are trying to rebuild West Ham."