The Belgian has been in prolific form of late and his manager believes it is difficult but not impossible for him to extend his contract at Goodison Park
Everton are keen to extend Romelu Lukaku's stay on Merseyside, according to manager Ronald Koeman.
Belgium striker Lukaku scored for the sixth time in the past three matches for club and country as Everton continued their unbeaten start to the Premier League season with a 3-1 win over Middlesbrough on Saturday.
Despite links with the likes of Manchester United and Bayern Munich during the close-season, his agent Mino Raiola said talks were in progress over a possible new deal at Everton.
And, speaking ahead of Tuesday's EFL Cup third-round match against Norwich City, Koeman suggested that the club were attempting to keep their star man at Goodison Park for the long term.
"The club is always trying to keep the best players," Koeman told reporters. "It's difficult but Everton is trying to keep him.
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"Romelu, I saw from the start in the pre-season when he was back after the Euros that he was really confident for this season.
"That [links to other clubs] is a part of the ambition, that's normal. It's good that players have ambition.
"It starts always with your own performance and everyone is happy to be part of Everton. That's not so difficult at the moment."
Lukaku will miss out against Norwich due to a minor toe injury, but is expected to be ready to face Bournemouth next weekend, while Koeman is keen for a tilt at silverware in the EFL Cup.
"Romelu is not available and only he is not fit for tomorrow," he said.
"He will have a rest with his toe for two days and then after two days he should be able to do normal training and be available for the weekend."
He added: "It's important, normally we can't win the [Premier League] title. Leicester last season is an exception. Then you have the EFL Cup, you have the FA Cup.
"We take it seriously. Of course, we will do some changes but all the players who will start are training hard to get an opportunity to play. We will have a strong team."