The midfielder has a release clause of around £25 million in his contract, and was targeted by Chelsea in the January transfer window.
Following David Moyes' departure to Manchester United, Fellaini has been linked with a move to Old Trafford and while Kenwright concedes the Belgian is able to move on, he insists no other players will be allowed to leave Goodison Park this summer.
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Leighton Baines has been a long-term target of Manchester United but Kenwright remains confident that the full-back, along with the rest of the Everton squad, will remain at the club under new manager Roberto Martinez.
“I’m as in love with this football squad as any Evertonian out there. They are this club and we don’t want them to go," he continued.
"They have worked massively hard for this club. Roberto doesn’t want them to go either. He’s got all of their phone numbers.
“He’s going to be on the phone to all of them saying: ‘We don’t want you to go.’ And they don’t want to go. Not one person has even half-indicated to me that the change will mean a change for them. Exactly the opposite – they all seem totally committed to it.
“So, yeah, I’m confident that squad, plus some Roberto signings, will form this football club’s squad for next season.”