Sporting Lisbon president Bruno de Carvalho claims Sullivan never had any intention of signing the Portugal midfielder.
Hammers boss Bilic wanted the Euro 2016 winner to boost his midfield and Sullivan insists he had a £30m bid rejected by Sporting.
But De Carvalho insists no official offer was ever made - and used his club’s TV channel to mock Sullivan and fellow co-owner David Gold’s links to the sex shop business.
He also poked fun at West Ham’s “fantastic results” so far this season and sarcastically suggested “they do not have a goalkeeper” after conceding ten times in three games.
But it is the accusation that Sullivan wasn’t really interested in Carvalho because he didn’t want to give Bilic what he wanted that is more controversial.
Bilic is under pressure after his side’s poor start to the season and was told his position was “under review” after a 3-0 defeat at Newcastle.
A sneering De Carvalho said: “West Ham supporters call Mr. David Sullivan and his brother D***o Brothers.
“What happened? They have had fantastic results, they do not have a goalkeeper and the president is very happy with the coach who was the person who wanted William.
“He wanted to sign the player the coach wanted so much, just like I would want to give a Christmas gift to my enemy - I wouldn’t want to give you anything!”
It is the latest twist in an increasingly bitter war of words which has already led to a threat of legal action.
Sporting director Nuno Saraiva last week insisted “no proposal arrived” from West Ham for Carvalho and described Sullivan’s claims as “lies”.
That prompted an angry response from Sullivan’s son Dave, who tweeted: “West Ham are commencing legal proceedings... as a written offer for the player was made”.
