The Everton manager has made no secret of his regard for 23-year-old front man, admitting he can go to the very top with further improvement likely in his all round game.
But it is his comparison to the best he has played with in his own stellar career at Ajax, Barcelona and with Holland, that elevates the praise higher.
"Yes he's one of the best, even comparing him to the players in my time," said the Everton boss.
Ronald Koeman holds Romelu Lukaku in the highest regard
Lukaku is the Premier League's leading goalscorer this season
"He is world class in his finishing. He is that good but he needs to improve in a total picture of a player – but that part of him is world class." Lukaku and Everton were "99.9 per cent" agreed on a new improved contact in December according to the player's agent Mino Raiola but frustratingly the deal remains unsigned.
However the club are once again hopeful they can get something done in the next few days with Koeman suggesting that they may be ready to announce progress after the weekend.
Koeman insisted such a deal would lay down an significant marker.
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"It [would be] really good and important for the club, for the team and for me because at the moment it means we can keep the best players and he has seen a future in this club. That is really positive." Everton travel to Middlesbrough tomorrow in seventh place trailing the Champions League places by seven points.
Despite starting with a seasonal target of a top six finish, a run of seven matches unbeaten has seen Koeman shift his focus a little higher.
"I have that feeling [we can shake up the top four] but it is always more difficult to show it than to talk about it. If we can keep our fitness, and I'm sure we can, then offensively how the team is improving, I think we do have opportunities.
"It is not that the first four teams are all playing the best football at the moment either and there is a high confidence in the team."