The Belgian forward spent last season on loan at Goodison Park and netted 15 times in 31 league appearances for the Merseysiders.
Lukaku has indicated that he wants to leave the Blues summer, with opportunties to impose himself at Stamford Bridge looking scarce as Jose Mourinho closes in on securing Diego Costa from Atletico Madrid, though the Toffees face stiff competition as the likes of Wolfsburg have also declared interest in the Belgian.
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"Romelu was a great addition to Everton, I have to tell you, off the pitch as well as on. He is an extraordinary boy. He speaks all those languages, he has got a terrific family and he walks the walk as well as talking the talk.
"We would love to have him back and people at Chelsea are good friends of mine, so we are hopeful but he's at the World Cup now and we will have to wait and see what happens at the World Cup."
Everton are also looking to secure another of last season's loanees, Gareth Barry, on a permanent deal, and Kenwright confirmed that manager Roberto Martinez had already spoken with the Manchester City player, who is out of contract this summer.
"Gareth Barry [is another] we would love to keep and that's ongoing work," he added.
"Barry had a great season for us. I know the manager has spoken to him and I will meet with his people and we are hopeful he will be here next season."