The Belgium international is the Premier League’s top scorer with 16 this season, including a superb four-goal haul in the 6-3 home win over Bournemouth last time out.

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Koeman said he was unsure whether agent Mino Raiola’s reported claim that Lukaku will sign a new deal was accurate, but welcomed the development.

Lukaku has been linked with a return to former club Chelsea, but Koeman hopes Everton can prove they are on the rise in order to keep their star striker.

“If the club and team is improving and showing ambition then it is always a good way for players to stay,” Koeman said ahead of Saturday’s trip to play Middlesbrough.

“That is what we need to show him so he is convinced that the future, or the short future, is at Everton.

“Normally players, if they really see a future in a club, if they see the team is improving, the team is getting stronger every day that is always a plus.

“We have had one or two conversations. The most important was at the start of the season when he came back from the Euros and then it was okay. 

“You need to explain [your ambition] to players and then they need to see it and you have to show it. At the moment it is really good and that gives players confidence to stay.

“I didn’t speak to the board about Romelu. If his agent mentioned that he likes to stay and is close or will sign a new a deal then that is perfect for Everton.

“We know everybody has his own ambition, that is normal, that is a human being. We like to keep the good players and he is one of them.

“At the moment he is top scorer in the league and playing at a high level. He is so clinical and it would be difficult to find a replacement for him. Because of that I hope he will stay.”

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Koeman thinks Lukaku is as good as it gets in front of goal, but feels the 23-year-old can still improve his all-round game.

He added: “Improving always starts with yourself. He is really a world-class finisher but in other detail, in other qualities, he can and must improve.

“He knows and that is the most important thing.”