However, according to ESPNFC this morning the big Belgian is now likely up for sell as manager Jose Mourinho looks to finance a massive move for Paris Saint-Germain and Uruguayan international forward Edinson Cavani.
The former Napoli star has already scored 19 goals in 27 appearances this campaign for the French outfit and while he would not be expected to be sold only a year after his move to Paris, money talks and lots of money pushes through transfers.
Lukaku's prolific goal scoring during his two most recent loan spells, last season to West Brom and currently at Everton has seen him score 26 Premier League goals in 53 showings between the sides in two seasons, more league goals than Fernando Torres has scored in 99 appearances since moving to Chelsea in 2010.
Why he would be considered a player not fit for Chelsea is only for Mourinho to decide, but Arsenal, Atletico Madrid and Tottenham are all thought to be hoping that the Blues will decide to sell to another rival in the league.
Although Martinez and the Everton board will hope they have the first shot at the 20-year-old, it is likely that he will go to a side that manages an offer that Chelsea cannot refuse.