The Toffees chairman is set to meet with the Spaniard but says the FA Cup-winning boss is not the only man on his list, nor is he the favourite to replace David Moyes
Martinez has confirmed he is set to leave Wigan and is currently the bookmakers’ favourite to replace Manchester United-bound David Moyes.
However, Kenwright is reported to be looking at other candidates, including Neil Lennon of Celtic, Malky Mackay of Cardiff and Vitor Pereira of Porto.
The Toffees chairman told Sky Sports News: “I will meet Roberto in the next 48 hours and he's on the list, as I've always said. No more than on the list.
“I said we'd be making a list, and Evertonians have been great as I indicated I thought they would be.
“There's no way I or anyone can say 'we'll get the right man' but I certainly will put everything into getting it right and getting the right DNA for Everton Football Club. That's very important.
“There is a list. No favourite - not at this moment.”
Kenwright revealed he has received a lot of input from the fans and insists he is pleased that they have been so supportive.
“They've certainly bombarded me with their thoughts and they're not a million miles away from mine,” he added.
“You always get the odd one that thinks he's got the only idea, and there are a few plumbers and electricians who think they can manage Everton, but in the main Evertonians and myself are sort of on the same page.
“The most gratifying thing is 90% of them said 'you didn't let us down last time, go with your gut instinct and hopefully you'll get it right again'.”