Lukaku, who left Chelsea for Everton in a permanent deal in 2014, has enjoyed a superb season for the Toffees and he currently leads the Premier League goalscoring charts with 21 goals.
The 23-year-old's current contract at the club runs until 2019, with the player recently admitting the best way to show just how good of a striker he has developed into is by playing in the Champions League.
Lukaku's former club, Chelsea, remain interested in re-signing him, though Bolasie believes Everton can convince the Belgium forward to stay at Goodison Park.
"I speak to Rom [Lukaku] every day and when a man has his plan, he has his plan. You can't really stop that," Bolasie told Sky Sports News.
"Players have ambition, as players they want to play in the highest team possible and Rom for me right now, at his age, is a world class striker and there aren't many about like him.
"I'm not surprised but I'm sure that Everton are going to find a way to deal with it."