Lukaku's current deal at Goodison Park expires in 2019, but the striker has made no secret of his desire to play in the Champions League and win major trophies.
The Belgian's former club Chelsea tried unsuccessfully to sign him last summer but Standard Sport understands Lukaku has re-emerged as a striking target for Blues boss Antonio Conte, who wants to bolster his attacking options this summer.
With Lukaku's long-term future at Everton uncertain, Chelsea legend Didier Drogba claimed he already knows where the 23-year-old will be playing his football next season.
But Koeman said on Thursday he doesn't know Lukaku's plans for the future although he revealed the striker - who currently leads the goalscoring charts in the Premier League with 23 strikes - will not extend his deal at Everton.
"He told me he won't sign a new contract," Koeman told a press conference ahead of Everton's game with Burnley on Saturday.
When then asked about Drogba's comments, Koeman replied: "No [I don't know where Lukaku wants to go].
"Maybe I wait for the call from Drogba to tell me where he wants to go."