Personal terms are already agreed between the player and the west London club, paving the way for quick negotiations with Everton.
Lukaku is pushing to find the exit door at Goodison Park this summer and is said to be keen to return to Chelsea, who are prepared to splash big money on him this summer.
Chelsea are thought to be ready to sell Spain worldwide Diego Costa despite the 28-year-old scoring 20 times in 35 games in Chelsea's title-winning season under Antonio Conte.
"Obviously the Costa thing has come out", Cole told Goal.
However, Lukaku is said to have told people close to him that it is his dream to return to Chelsea. I like Lukaku. I'd take Lukaku, he is like for like with Costa, but they only need one or two players and just keep the continuity going. He is younger [than Costa], that's in his favour'.
Joe Cole says Chelsea should "not look outside" a trio of strikers now in the Premier League. Morata is another one but he has never played in England so there is a little question mark there.
Ronald Koeman is targeting a new striker, with Romelu Lukaku's future in doubt, and has now reportedly set his sights on Dembele.
Both Costa and Lukaku finished behind England worldwide Kane in the race to the Premier League's golden boot after the Tottenham star netted 29 times in the top flight last term. In 48 games played, he has scored 32 goals, and this record has attracted much attention for this 20-year-old.