"I didn't speak to the board about Romelu but if his agent has mentioned he likes to stay or is close to a new deal then that's perfect for Everton," said Koeman.
"If players see a future at the club, if they see the team improving and getting stronger then that's always a plus for them to stay.
Everyone has their own ambition, that's normal, and we like to keep the good players. At the moment he's the top scorer, playing at a high level, so clinical, and it would be difficult to find a replacement so I hope he stays.
"He's a world class finisher but in other details, other qualities, he can and must improve and he knows that. If the team's showing ambition it's always good and we need to show him that the short future is at Everton."