The news comes after Sullivan, along with ex-co-owner David Gold relinquished their stakes at St Andrew's to Hong Kong businessman Carson Yeung on Tuesday.
Sullivan insists he is keen to stay in the game after taking what he describes as a "well earned break", but has refused to speculate on whether he could be mounting a bid for the cash-strapped Hammers.
He told Sky Sports News: "I wouldn't discuss any possibilities with any clubs but I will look at what's available in the next three to six months and if something appeals to me on an emotional point of view or financial point of view, ideally both - I would immediately step in and buy a percentage or controlling interest in that club."
Sullivan, who confessed "anything's possible in football" regarding a potential investment at Upton Park, understands why he has been mooted with a future takeover.
He added: "I just think I'm being linked because they are down the road (from me) and they are obviously owned by a bank that's insolvent, but I have had no discussions whatsoever with West Ham and I have had no discussions with any other club at this stage."
Sullivan has confirmed that new Blues owner Yeung will appoint a high-profile chief executive as the new owner is keen to take the West Midlands club to new heights.
"That's exactly what we've heard," he said of the person set to take over Karren Brady's role at the club. "We were told it is someone from the Premier League.
"All we know is they're keen to buy players - they indicated they would have liked to have brought some players in August had they brought the club in time.
"They've indicated they are possibly looking a new stadium, all the things we would have liked to have done and we hope they do it for the supporters."