The 23-year-old Belgium international joined the Premier League club on loan from Chelsea in 2013 before making the move permanent in an Everton record 28 million-pound ($34.8 million) deal in 2014.
British media reported that Lukaku asked for a transfer this year but he remained at Goodison Park and has scored seven league goals this season.
"His potential is greater and higher than Everton as a final destination," Koeman told Belgian newspaper HLN.
"If Romelu was to play at Everton until the end of his career I know he has left something behind," the Dutchman added.
"I gave him confidence and he has himself recognised that it was good for his development to play another year at Everton. What after this season comes, no-one knows."
Koeman likened the powerful Lukaku to former Netherlands striker Patrick Kluivert who he coached at Barcelona.
"Kluivert was also a striker who was quite young when he was in the picture and had a fantastic career. Eventually, Kluivert played for Barcelona which could happen with Lukaku," Koeman said.
"Lukaku 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."
Lukaku, who started his career with Anderlecht before joining Chelsea in 2011, has scored 17 goals in 52 internationals.
(Reporting by Ed Osmond; Editing by Toby Davis)
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