The loanees played a pivotal role in the Toffees successful season which saw them narrowly miss out on Champions League football.
Lukaku, 21, scored 15 goals in 31 appearances for the Toffees last campaign and has become a fan favourite.
Everton boss Roberto Martinez, who signed a new three-year-deal at Goodison yesterday, is keen to retain the services of Lukaku.
But it looks increasingly likely that the Belgian international won't be playing his football in Liverpool next season as the striker has been heavily linked with a move to Atletico Madrid to replace the out-going Diego Costa.
Martinez's desire to keep Lukaku has been echoed by Kenwright, but the 68-year-old knows the club face an uphill struggle to keep the highly coveted striker.
He said: “Romelu was a great addition to Everton. I have to tell you, off the pitch as well as on, he is an extraordinary boy. As you know he speaks all those languages, he’s 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 is at the World Cup now and I think we will have to see what happens at the World Cup.
Kenwright is also keen to keep Manchester City loanee Gareth Barry.
The ex-England international had an impressive spell at Goodison last season after being told City boss Manuel Pellegrini that he did not fit into his plans.
Kenwright said: “Gareth Barry had a great season for us and I know the manager has spoken to him and I will meet with his people and we are hopeful that he will be there next season.”
Tottenham Hotspur are reportedly set for another season of heavy spending in the transfer market, with Chelsea Romelu Lukaku believed to be high on the list of transfer targets for new boss Mauricio Pochettino.