The Toffees striker, who nwtted 26 goals last season, looks certain to leave Goodison Park this summer and has been heavily connected with a return to Chelsea, while Manchester United are also on queue to grab him.
United boss Jose Mourinho, who worked with Lukaku during his reign at Stamford Bridge, is seriously on the lookout for a replacement for Zlatan Ibrahimovic, while the Belgian has also been tipped to take Diego Costa's place at Chelsea.
The 24-year-old is desperate to play in the Champions League, something that both clubs can offer, and according to the report in the Daily Express he knows exactly where he wants to be come next season.
“My agent knows what’s going to happen,” the 24-year-old told Sky Sports.
“I know what I want to do, and whenever something happens, you guys will know.”
His agent, Mino Raiola, recently confirmed that Everton will allow Lukaku to go only if they get the right offer for the player.
“Lukaku had a promise that if certain clubs came this summer that he could leave this summer,” Raiola told talkSPORT.
“We are not in concrete talks with anybody at this moment, but hearing the market I think some clubs will contact Everton.
“If the price is right for Everton and the project is right for Lukaku then I think he will want to make another step, but we are not there yet.”