Calvert-Lewin scored the opening goal in Everton's 4-0 demolition of Hull on Saturday - and supporters were mightily impressed by his display.
And Koeman has vowed the comments made by the Belgian global have not made him nervous as he still has time to run on his contract. It's up to the club to get the deal over the line'.
Lukaku publically questioned the club's ambition in the days preceding Saturday's contest to cast doubt over his Everton future, but the Belgian added the gloss to a convincing victory as he moved top of the league's scoring charts with a late double at Goodison Park.
"To do that, you need the platform to show yourself", he said when asked about his desire to be ranked along with the world's best forward. Everybody knows you can't do this in one year, it takes time. The rest has to be done with the board and the manager.
"We try to get the best players, but a lot of them want to play Champions League and we are not playing Champions League at the moment".
He said: "But I think everybody needs to understand ambitions, and his situation I've tried to explain".
Everyone see the difference between this season and last and it is impossible to do this in one transfer window in one season. There is always competition.
"Just buying better players doesn't mean you will play in that tournament, because Manchester United, City, Liverpool or Arsenal won't qualify and they spent money for that".
'I spoke with Rom about the project in the summer.
Lukaku, who still has two years to run on his contract, retained the backing of Everton's supporters, who loudly cheered his name before kick-off.
"What you don't like every day talking about his contract".