Kenwright said the club have reached their limit when it comes to borrowing from the banks and that only a buy-out could currently solve the problem.
"We've come to a stage with our bank with our finance where we just can't borrow any more," he said.
"I've said year after year, what we do is we beg and borrow from the bank. That's what we've been doing.
"The banks are tightening in now. We just can't borrow any more money, a: to protect the football club and b: to protect the fans.
"We've got a lot of people out there, committed people like Keith Harris (who has brokered the sale of a number of clubs), like banks, agents, lawyers, trying to find the buyer.
"I thought about saying the right buyer for the club - of course it has to be the right buyer - but we're actually trying to find a buyer for the football club.
"We haven't got that billionaire or even multi-multi-millionaire because I'm neither of those things and we really do need the buyer that we have been searching to find for three years.
"The maths is simple; we've actually got an income up to £80million but the costs are £85million so you don't need a calculator to work out what the problem is."
However, Everton's difficulties appear to run much deeper than that if reports from a fans group are to be believed.
The Blue Union held a meeting lasting nearly four hours with Kenwright in which the Everton chairman was particularly candid about the current situation.
Those supporters published a transcript of their get-together on the internet - much to the annoyance of the chairman, who believed he was speaking in a closed environment - in which they make a number of claims.
According to Blue Union, Kenwright told them he had signed a deal with the banks to prevent them from stopping the club trading after claiming the financiers asked him every week how the sale process was progressing.
That in itself is a difficult task, as near-neighbours Liverpool discovered before they eventually found Fenway Sports Group just under a year ago.
The supporters' group claim Kenwright related one anecdote of how two men came forward and did due diligence only to be exposed as hoaxers with one of the men reportedly not a high-flying executive with a global firm but actually living in a one-bedroomed flat.
Blue Union's account of events also suggested that despite the requirement to sell players to raise funds Kenwright said there was a core quartet of Phil Jagielka - for whom Arsenal have already made a bid - Leighton Baines, Marouane Fellaini and Tim Howard who were untouchable.
Neither Kenwright nor Everton have commented on the claims by Blue Union but Press Association Sport understands privately club officials are deeply unhappy with the actions of the fans group.
However, the Toffees chairman freely admits they fully expected this summer to be a difficult one in terms of transfers with the club yet to make a signing.
"The world is in a recession and I don't know any business that isn't suffering at the moment and I include football in that, other than the financial elite," he told Sky Sports News.
"We knew this summer we were going to get to a point where things were going to get very tight.
"We knew we had to trade. There has not been a lot of trading in football itself this summer.
"We've not been able to trade yet and that's the reason that we've not bought in a new player."