The 20-year-old has scored 14 goals in 30 Premier League appearances during his temporary switch from Chelsea, with Martinez keen to secure his services beyond the end of the current campaign.
The Spaniard is prepared to wait until after Lukaku has featured for Belgium in Brazil to discover whether he will be able to keep the powerful front-man and is not concerned about being priced out of a move for the Chelsea youngster.
"I don’t think that's my worry," he is quoted as saying in the Liverpool Echo. "The worry would be that if the deal was a cheap one, it would be because he has had a torrid time and hasn’t fulfilled his potential.
"The reason Romelu came to Everton was for him to take a big role, take a lot of responsibility, to start playing 90 minutes and be a real brain in that forward line, and he has done that so we couldn’t be happier.
"The parent club, Chelsea, are delighted with his progress and the player has developed an incredible relationship with our fans.
"His memories will never evaporate, but we will see what's next.
"We'll see what’s the best thing for everyone. But everything will be in stages: how Chelsea are doing in their own squad and how that frees some players. It's going to take a bit of time and I don't think Romelu's situation is going to be resolved before the World Cup, in truth.
"I think it will be after the World Cup."
