The Hammers have clashed with Spurs over a potential move into the 60, 000 capacity stadium in Stratford – just three miles down the road from Upton Park.
And Sullivan insists that a move from their rivals to the stadium could spark civil unrest among supporters.
“It would be such a slap in the face to East London,” Sullivan told the Daily Mail.
“If it happens, there will be real problems that could easily lead to civil unrest.
“I think there could be riots, such is the ill feeling between West Ham and Spurs and I know the police feel the same.”
Sullivan then went on to claim that Spurs “pinched” Eidur Gudjohnson from West Ham last season.
“I feel very let down by Tottenham,” Sullivan revealed. "The way they do business is not right.
“They pinched Eidur Gudjohnsen off us after we brought him from Barcelona for talks. He just disappeared from the hotel. And the way they unsettled Scott Parker was appalling.
“Now they want to move into our borough of Newham. How would they like it if we suddenly set up a new home in Haringey. I'm flabbergasted by the cheek of it.”
Meanwhile, Hammers boss Avram Grant is confident that his side will stay in the Premier League after their recent improved form.
“We are not a team to be on the bottom of the league,” Grant told Sky Sports.
“We are not heading for relegation. We play football to be in a better place and we will do it."
By Luke Nicholls
