The powerful Belgian spent last season on loan at Goodison Park, netting 15 Premier League goals as the Merseysiders narrowly missed out on a surprise top four finish.
Despite his impressive form, Chelsea are rumoured to be ready to let him leave either on a temporary or permanent basis this summer, which has alerted Everton.
It was reported that the youngster has his heart set on Champions League football, but prospective moves to Atletico Madrid and Juventus appear to have collapsed.
This has lured Roberto Martinez back into the running, with the Spaniard known to be desperate to get the 21-year-old back.
Lukaku is set to link up with Chelsea this week, where he will hold crunch talks with Jose Mourinho in a bid to clarify his future.
Everton are also keen on a loan deal for Blues winger Christian Atsu, but in order to push such an arrangement they would need to snap up Lukaku on a full basis due to not being allowed two players on loan from the same club at the same time.