He fears West Ham could repeat the demise of Newcastle, who were relegated from the Premier League in 2009 after a season of off-field turmoil.
"We are going to ask everyone at the club to voluntarily take a wage reduction," Sullivan earlier told BBC Sport.
"I can't believe the contracts I've inherited. The club is in a mess and we all have to pull together. If we go down, I can't even consider the situation.
"It'll be Armageddon if we go down. It'll be worse than what's gone on at Newcastle."
Sullivan revealed that Zola would be among those expected to take the cut, and added that anyone unhappy with the request could leave the club.
"Gianfranco is highly paid and I think all managers in the Premier League are overpaid," said the Hammers' co-owner.
Zola, who earns an estimated £1.9m a year, stated he was not at Upton Park for the money.
"It is about working for something positive. I always enjoy working for this club. The money was something that came after," he said.
Sullivan had earlier said: "Everywhere you look there is excess. Everyone is overpaid for the job they do. There are 110 mobile phones being paid for by the club and you have minor people with Blackberry phones and other types.
"Already members of the administrative staff have come to us and said, 'look we know we are overpaid for the job we do but we are good people and we'd like to stay and we are prepared to take a voluntary wage cut'."
Sullivan and co-owner David Gold, who left Birmingham in November following Hong Kong businessman Carson Yeung's takeover, took control of West Ham last month after buying a 50% shareholding.
West Ham's new owners say they have uncovered the severity of the club's financial position over the past few weeks.
They are actively looking to reduce the club's debts, with professional investors being approached for finance and the club have already had to make several people redundant.
All I need now is for the team to start winning. Wednesday night will do for starters
"We had a player liaison officer who just drove a few of the players around and he was paid £50,000 a year," revealed Sullivan.
"We've had to make people redundant, we'll make other people redundant. There are people at the training ground who we don't even know what they do, there are so many people there. When we spend money we have to make it count."
West Ham also have to make their home games count, and they will be desperate to pick up vital league points against Birmingham in a match given added significance because of Sullivan's and Gold's links with the two clubs.
The manner of Gold's departure from St Andrew's still causes angst, with the 73-year-old upset that he was not retained as chairman when Yeung took over.
"I was at Birmingham City for years but I really want to give them a good whacking," he said.
"I have great fondness for them, but it was sad the way it ended. They reneged on the decision to keep me on the board - that will always rankle.
"After 17 years at Birmingham, I think we know how to run a football club, I am certainly a lot wiser than when I first started.
"All I need now is for the team to start winning. Wednesday night will do for starters."
The past and present regimes at Birmingham have been involved in verbal spats over the past few months but Yeung's representative, Peter Pannu, said there will not be any bad blood on Wednesday.
"The other party have taken over at West Ham and we wish them well. In fact, I did congratulate them myself," Pannu told the Birmingham Mail.
"We are, after all, football people but work is work and we have to delineate on that very clearly.
"I will shake hands in the boardroom. I have no problem with that and I have had a chance to have a conference with David Sullivan and David Gold.
"We had a very candid chat. David Sullivan appears to be a very straightforward man. He speaks his mind - just like me.
"I think people must understand we are all professionals so we know how to differentiate between right and wrong, work and personal.
"I respect David Sullivan, he has got his stance, we have got ours and we agree to disagree."
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