Parker, 29, has been a long-term target for Spurs boss Harry Redknapp and had hoped to lure his former club into parting with their prized asset.
But Sullivan told the club's website that the England midfielder is not for sale at any price.
“I made a promise that I would not sell Scott and I will not, for any amount of money, break that promise to the West Ham supporters,” he said in a club statement.
“Scott is not for sale at any price, to anyone. West Ham supporters, for far too long, have had owners that sell their best players and promise one thing and do another.
“This a new era. We are building a bigger, better West Ham and we make a promise, we honour it.”
Parker moved to Upton Park in a £7 million deal from Newcastle in 2007 having previously played for Chelsea and Charlton and has three-years left on his current deal, with the Hammers making their stance on the possibility of Parker leaving for White Hart Lane, or anywhere else, perfectly clear.
“The club would like to state that regardless of the size of the bid, nothing will break the promise that chairman David Sullivan made to our supporters,” the statement continued.
“As repeatedly stated, Scott Parker is not for sale and there are no circumstances and no amount of money that will cause us the break that pledge to the fans.
“The club informed Tottenham chairman Daniel Levy prior to him making the offer that we would not welcome any approach to unsettle the player.
“Scott has three years left on his contract and the club has opened talks with his agent over a new five-year deal.”
West Ham will be looking to improve on their 17th place finish of last season in the coming campaign, while Spurs will aim to make the group stages of the Champions League for the first time.
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