The Merseyside club has been quiet over the summer, with no notable signings going through.
While Everton midfielder Mikel Arteta has admitted that he hopes new signings will arrive at Goodison Park before the window closes, Kenwright has revealed that their bank will not allow them to borrow any money for players.
"Two things. One, 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.
"Two, we've come to a stage with our bank with our finance where we just can't borrow any more. The banks are tightening in now. We just can't borrow any more money.”
The 65-year-old said that the lack of outgoing players has proved a stumbling block in bringing new additions into the club.
"We knew this summer we were going to get to a point where things were going to get very, very tight,” he added.
“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."
Everton host newly-promoted QPR at Goodison Park in their first Premier League fixture on Saturday (August 20).