The 22-year-old's father, Roger, has told Het Laatste Nieuws that his son is ready to move on and join a bigger club at the end of the season, claiming interest from Juventus and Manchester United among other clubs.
"I think he must choose Manchester United or Bayern Munich. Manchester United is a team under construction with no real focus."
Lukaku himself has told Sky Sports that he is ready to take the next step in his career and play for a Champions League club.
"That is the next step for me," said the former Chelsea youngster. "I'm 23 next summer and I think it would be nice to play in the Champions League from next season."
Liverpool legend Fowler seems to have suggested on Twitter that Lukaku could leave Everton in the summer transfer window.
Doesn't bode well for @Everton that lukaku interview ...— Robbie Fowler (@Robbie9Fowler) March 26, 2016
Losing Lukaku is going to decimate Everton’s quality in attack, and that is only going to be good for Liverpool.
After all, Liverpool and Everton are fierce Merseyside rivals, and the Reds fans will be delighted to see the Toffees lose one of the best players.
Fowler grew up as an Everton fan, as he told Goal.com back in March 2009, but he has been a Liverpool supporter since he joined the Reds when he was 11 years of age.
Lukaku has scored 18 goals and created 47 chances in 29 Premier League appearances for Everton so far this season.