"There's no transfer fee involved and he's got the choice of almost every club in Europe. He has played at the highest level," Sullivan added.
"We can carry one exceptional player, who would make a difference on that wage, but generally we have to bring the wages down and in the summer we would hope to sign younger players on a fraction of those wages.
"We have looked at a few players in the Championship but the reality is that it is no good if they make the grade in 12 months time, we need them to make the grade now.
"We have a crisis and you have to have a different strategy to what our long-term strategy will be."
Sullivan has reportedly targeted two strikers and a defender to sign in the January transfer window as he tries to get West Ham out of relegation trouble.
They are currently 16th in the table and are on the same number of points as Hull, who are in the relegation zone.
"We are trying to sign players because unfortunately we have come in very, very late and we have got a very unbalanced squad," added Sullivan.
"We are particularly short of strikers and they are the hardest and most difficult position to fill. That's the short-term objective.
"We have guaranteed that we will not sell a player in the transfer window and we are looking at targets. We are doing our best for West Ham but at the moment we are drawing blanks.
"It's a difficult time to sign players but the club desperately needs strikers and we have to bring some in."
Gold and Sullivan, who left Birmingham City in November following Hong Kong businessman Carson Yeung's takeover, took control of the Hammers on Tuesday in a deal which concluded a long-running saga over the club's ownership.
At the media conference to announce the takeover, Sullivan revealed the scale of West Ham's debts and he re-iterated on Thursday that the club "from top-to-bottom" is "very inefficient".
There is no other club we would have taken on this liability for and risked a huge amount of money for - we could lose the lot
Asked how much of a crisis it would be if West Ham were relegated, Sullivan replied: "It would be absolutely horrendous, that's all I can say.
"It doesn't even bear thinking about. It can't happen and it must not happen. That's why we are doing everything in our power for it not to happen."
Sullivan suffered relegation and promotion with Birmingham but he believes the drop has bigger consequences for West Ham than it does to his former club.
"Birmingham is a much smaller club, it does not have the same potential as West Ham," he said.
"We never took on the wage bill at Birmingham, where the highest paid player is on £25,000-a-week. If they got relegated it wasn't pleasant but you could take a season of it because it was built into the equation.
"We've inherited a situation at West Ham where it's not built into the equation in any shape or form.
"If we weren't supporters we wouldn't have taken it on. There is no other club we would have taken on this liability for and risked a huge amount of money for - we could lose the lot."
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