The Toffees have been long-term admirers of Wigan manager Roberto Martinez, while Porto boss Vitor Pereira is also 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.
And 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.