The pair enjoyed successful loan stays at Goodison Park last season, and Belgium international Lukaku finished top of the club's scoring charts with 15 goals for the Blues.
The evergreen Barry also won widespread plaudits for his displays in a sitting midfield role, and the former England star made 32 appearances last term as Everton ran Arsenal close for the final Champions League place.
Blues owners Kenwright has admitted that he is working hard to keep both players at Goodison Park next term, but accepts that he is unlikely to retain Gerard Deulofeu, who will head back to Barcelona.
Kenwright told Sky Sports: "Who's to say what happens with Deulofeu next season? We don't know. But there will be other players that Roberto will be looking at. Lukaku we would love to keep, Gareth Barry we would love to keep and that's ongoing work, and we obviously have to add to the squad, so that's non-stop."
"Romelu was a great addition to Everton. I have to tell you off the pitch, as well as on, he's 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're hopeful. But, he's at the World Cup now, so I think we'll have to wait and see what happens."
"Gareth Barry had a great season for us and I know the manager has spoken to him and I'll meet with his people and we're hopeful he will be there [at Goodison Park] next season."
Lukaku has been linked with a move to Atletico Madrid this summer, but the La Liga champions are only thought to be considering another loan move.
However, with Lukaku enjoying a fantastic campaign on Merseyside last term, coupled with Kenwright's friendship with the Chelsea hierarchy, perhaps the burly Belgian could be set for another short-term stay with the Blues?