The Toffees' chief believes a hard-working manager will be the best option to take over at Goodison Park after David Moyes joins Manchester United in July.
The Toffees have been long-term admirers of Wigan manager Roberto Martinez, while Porto boss Vitor Pereira is also reportedly on the radar. Gus Poyet, Malky McKay and Neil Lennon have also been linked with replacing Manchester United-bound Moyes, who will take over at Old Trafford on July 1.
Kenwright says the names linked with the soon-to-be vacant post are accurate.
"I have got people in mind," Kenwright told The People. "A lot of those mentioned are not too far away. Everton have got a type, it's a very hard-working industrial football club."
Wigan chairman Dave Whelan is set for talks with Martinez next week, but has claimed that Everton are not "big enough" for the Spaniard.