However, the Belgian dropped a bombshell when he told Ronald Koeman that he would not extend his current deal at Goodison Park, which expires at the end of 2019. His determination to play in the Champions League is thought to be a key reason in his decision not to resign at Everton, who last appeared in the competition in 2005.
And Lukaku’s team-mate, Yannick Bolasie, has admitted that there is little Everton can do to persuade Lukaku to stay if he has his heart set on a move away from Merseyside.
"I speak to Rom every day. When a man has his plan, he has his plan, you can't really stop that,” said Bolasie, who signed for Everton from Crystal Palace in a £25m deal last summer.
"A player's got ambitions. The best players, they want to play in the highest team possible and Rom right now is a world-class striker and there aren't many about like him.
"But I'm sure Everton are going to find a way to deal with it."
Bolasie is still recovering from a cruciate knee ligament injury he suffered in December, in just his 13th Premier League appearance with his new club.
The Congolese winger is not expected to return until well into the new campaign and has some words of comfort for Seamus Coleman, who is set for a similarly lengthy spell on the sidelines after having his leg broken while on international duty with the Republic of Ireland.
"Everyone's just showing great support,” Bolasie told Sky Sports News.
“The club have been supportive with me, especially the manager and staff, so I'm sure it's going to be the same outcome for him.
“He's a strong character so I can see him coming back better."
It had been reported Bolasie could be out until 2018 after undergoing surgery first to repair his meniscus and then the cruciate ligament.
But the 27-year-old is optimistic he will be back sooner.
He added: "I'm seeing the light right now. I'm in a good place with rehab. I can't actually put any time schedule down, but I'm pretty confident that I'll be back before 2017 ends, that's for sure."