The Blues boss has admitted he does not know if Lukaku will stay at Goodison Park beyond next summer after the Belgian agreed in August to remain at the club for another season following speculation linking him with a move away from Merseyside.
Lukaku will need to leave Everton to fulfil his potential
Lukaku has scored seven of Everton's 15 goals in the Premier League this season and, while Koeman will be hoping his star man will stick around, he told Belgian newspaper HLN that in the long-term Lukaku should be aiming for bigger and better things.
Koeman said Lukaku has the potential to become "an amazing striker. He is still only 23-years-old and is only going to get better". However, the Dutchman admitted Lukaku's potential is "greater and higher than Everton as a final destination."
The former Southampton boss added that if Lukaku was to play at Everton until the end of his career then "he has left something behind." The Dutchman said that Lukaku has "recognised that it was good for his development to play another year at Everton" but he admitted that "no-one knows" what will happen after this season in regards to Lukaku's future.
Lukaku, who is under contract at Goodison Park until 2019, first joined Everton on loan from Chelsea and he has scored 68 goals for the Merseyside club in 137 appearances. His 50 goals put him third on Everton's list of top scorers in the Premier League era, behind Tim Cahill on 56 and Duncan Ferguson on 60.
Patrick Kluivert comparison
Koeman believes Lukaku has the potential to one day play for Barcelona and drew comparisons between him and former Netherlands striker Patrick Kluivert, who Koeman worked with during spells coaching with the national side, at Barcelona and later as manager at PSV.
The Blues boss said that Kluivert was also "a striker who was quite young when he was in the picture and had a fantastic picture". Kluivert scored 90 goals in 182 appearances for Barcelona and Koeman said that he can see Lukaku doing the same and playing for the Catalan giants during his career.
Koeman added that he believes Lukaku as a player is "quite complete" in the way that he can "hold a ball and be a target man and because, he is tall and physically strong, you can play directly with the long ball."