Lukaku, 23, picked up the Players' Player of the Season award and the Player of the Season trophy -- chosen by Everton fans -- at the club's end-of-season awards night on Tuesday.

The Belgium international, linked with a summer exit from Goodison Park, has scored 25 goals in all competitions, with 24 of those coming in the Premier League.

He said he was "not always an easy guy" and thanked Koeman for helping him reach "the next level."

Lukaku leads the race for the Premier League's Golden Boot, having scored three more than nearest rival Harry Kane of Tottenham with two games remaining -- although Spurs have a game in hand.

"I'm very happy," he said in a speech accepting the awards. "I want to thank the manager for pushing me, even though sometimes I'm not always an easy guy. He's taken me to the next level.

"As a young guy I just try to learn every day and give my best. Sometimes there are ups and downs, but it's always with the best intentions.

"I want to help my teammates win and I have tried my best this season. I want to thank the fans as well."

Lukaku said he had expected Idrissa Gueye to win the Players' Player of the Season award.

"I'm surprised to win. Since I turned professional, this is the first time I've won this award," he added. "I thought Gana was going to win because he has been the best player consistently.

"He and the other midfielders this year gave more licence to the likes of me, Ross Barkley, Kevin Mirallas and Yannick Bolasie to create and score. As a team we are back on track and the future looks bright."

Lukaku's goals this season have also seen him overtake Duncan Ferguson to become Everton's all-time top scorer in the Premier League era.

He said: "I think everybody is playing at a high level and I look at the improvement of Ross, who inspires me day in, day out. Gana came in from a team that got relegated [Aston Villa] and being a main man in midfield has been impressive.

"Also Jags [Phil Jagielka] -- he was out the starting lineup but has led the team."

Koeman has said he is calm about Lukaku's contract situation, despite increasing speculation about a potential return to Chelsea and reported interest from Manchester United.

The 23-year-old has two years remaining on his current deal, and chairman Bill Kenwright said he hoped Everton would "see many more goals from you."

Elsewhere, it was also a successful night for Everton midfielder Tom Davies, who won the Young Player of the Season award, as well as the Individual Performance of the Season trophy for his display against Manchester City and the Goal of the Season award for his strike in the same game.