Proposals for a £400million, 50,000-seater stadium and shopping complex in Kirkby, in association with Tesco, were rejected by Communities and Local Government Secretary John Denham.
Kenwright said they were happy to remain at Goodison Park but until the necessary finance could be generated - which the current board is unable to do - their options were limited.
Fallen through: Everton's hopes of moving to Kirkby were dashed this week
A ground-share with near-neighbours Liverpool - who themselves are having financial difficulties funding a new stadium - has been raised again but neither club is particularly keen on the prospect.
The search continues for a major cash injection and the chairman has repeatedly stressed he would immediately step aside for the right investor.
'The first thing to say, in terms of Kirkby, is that the chapter is over and the book is closed,' he said.
'The motivation has only ever been to improve the finances of the football club. They need to be stabilised, improved and expanded.
'As everyone knows, the club doesn't currently have a chairman or a board in a position to do those things.
'We have had some of the best financial experts helping us with our search for investment for some considerable time now - and that will continue.'
Kenwright added on the club's officical website: 'Inevitably the search will throw up questions about where the club will play its football in years to come.
'And the response will be: "We are happy to be at Goodison Park while weregroup, reassess and consider all options available to us there and possiblyelsewhere'".
'At the end of the day, the club's finances will be key to everything.'
Everton demand talks after Kirkby axe and Liverpool rule out ground-shareMoyes had sights set on top four. but injury-hit Everton are near drop zoneEVERTON FC