However, West Ham were the first London team to make a move for him following the sacking of Sam Allardyce at the end of last season.
Sullivan has previously revealed various high profile managers he went after before opting for Slaven Bilic in the summer, including the likes of Rafa Benitez and Jurgen Klopp.
And West Ham are now preparing to face Conte in the Premier League next season when he replaces interim boss Guus Hiddink at Chelsea.
Even though he rejected the chance to come to Upton Park, Sullivan remains full of admiration for Conte.
The 67-year-old added: “He’s a got a massive record of winning things. He’d have had great connections in Italy, played sexy football and it would have been be jolly good.
“With a team like Chelsea you have to bring in a manager who has won things at a top level. You can’t take a risk.
“I’d stay with Slaven now. You stick with what you know.”
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