With manager David Moyes working on a tight budget and the pressing need for a new stadium, Kenwright has long accepted the Toffees require a huge injection of capital.
However, he pointed out that even if there was a wealthy benefactor out there, the club had to learn lessons from other takeovers which had not gone exactly to plan.
"The truth is that Everton do need a billionaire. Of course that's a stock phrase, but we do need major investment," said Kenwright.
"One of the difficulties of being a chairman, who has had to use money as wisely as he possibly knows how, is that it's hard when you get bombarded, as I have been in the last three AGMs, with questions like 'Why can't we have what Newcastle have? West Ham? Portsmouth?'
"Am I hopeful? I've been hopeful before, and nothing's come of anything. But I will find that investment."