In an extraordinary press conference, the Hammers boss admitted he laughed at the pair being insulted by Sporting Lisbon president Bruno de Carvalho.
And he also denied claims made by Sullivan that he turned down the chance to sign Grzegorz Krychowiak and Renato Sanches, insisting they were never main targets.
The pair went on to join West Brom and Swansea respectively as West Ham missed out on signing William Carvalho.
The Hammers’ failure to sign the Sporting midfielder for a deal in excess of £24 million led to a war of words between the clubs leading to the dig at the former soft porn businessmen from De Carvalho.
“I thought about coming with a lawyer today,” said Bilic, whose bottom-of-the-table side face Huddersfield on Monday.
West Ham's Manuel Lanzini shows off impressive shooting skills
There have been issues David Sullivan likes to talk – it’s his right to be able to
West Ham boss Slaven Bilic
“There have been issues David Sullivan likes to talk – it’s his right to be able to.
“I wanted the player [Carvalho] and that is not exactly what happened with those two you mention.
“I wanted Carvalho and it looked likely, and to be fair, during my time at West Ham, it’s very common that when it looks like a player is going to happen, that two or three other names someone throws in and that distracts you from the main target, and that’s what happened.”
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