Among those being linked with the job are Alan Stubbs, David Weir and Duncan Ferguson - all former Everton players that are presently part of the backroom team.
And asked today if he would recommend members of that team to Kenwright, new Manchester United manager Moyes said: "I would always recommend the people who are around me.
"A lot of them know how the workings of the building (at the training ground) are, how we move things forward and the restraints the club has, so it is easy for them to deal with that.
"We (Moyes and Kenwright) speak a couple of times on the phone, and if he has anything to say or wants me to help him, I will do so."
The 50-year-old stressed his confidence that Kenwright will "get it right" when he appoints the new manager, and Moyes added: "I think continuity at every club is important.
"You can't always just have a complete clean slate and start again.
"But these are questions you need to wait to ask the chairman about when the time comes."