Sullivan left Blues as a result of Carson Yeung's takeover at St Andrew's last week and has been linked with a move for his beloved Hammers.
The 60-year-old admitted he has done some background checks on the Hammers' financial position but ultimately has not held talks with anyone.
"Well West Ham is a club close to my heart, a club I supported as a boy, a club I would dearly love to be involved with," he told Sky Sports News.
"But I have had no discussions with West Ham. From an outsider looking in and the debts that appear to be at West Ham look absolutely huge so I'm not sure I could face what's going on there.
"But West Ham does need help and it does need help very quickly. They are in the bottom three of the Premier League.
"I hope someone gets involved quickly within the next week or month or two otherwise West Ham could be in the Championship or bust or both but as I said I have had no discussions but time will time.
"I've done as much homework as I can do without being privy to any of the figures.
"You speak to people who used to be there you read accounts that are 12 months out of date but there is only so much you can do.
"But it is something I would look at if I was given the opportunity but at this moment in time I have done nothing and to be quite honest I'm happy to have a month or two off because football is pretty stressful and West Ham will be very stressful for whoever gets involved."
Having spent 16 years at Birmingham, Sullivan admits he is desperate to get back into football and added that former Blues partner David Gold, who has also left St Andrew's after the offer of honorary chairman was withdrawn, could join him on a new venture.
"I think David would definitely want to stay in football and like me will be involved in another club within six to 12 months maybe sooner," he declared
"I think there is a strong possibility, but not a certainty, David might want to buy his own club he might want to join with me and buy another club.
"There is a distinct possibility we could be together at another club."
Stoke 11/10, Draw 9/4, West Ham 13/5