Those performances could trigger interest in his services, and given that Everton have been forced in to selling the likes of Joleon Lescott, Mikel Arteta, Jack Rodwell and Marouane Fellaini in recent years, there are growing concerns that Lukaku could become the latest big name to leave Goodison Park.
A mid-season deal would be unlikely, but that seemingly hasn't stopped manager Roberto Martinez from eyeing potential cover for Lukaku, should he leave the club or even get injured, even with Arouna Kone offering support in attack.
The Sun now report that Martinez has become a keen admirer of Sheffield Wednesday striker Lucas Joao, who only joined the Owls from Nacional over the summer.
The 22-year-old striker, born in Angola, has impressed during his time at Wednesday, and even got his name on the scoresheet in the 3-0 Capital One Cup win over Arsenal last month.
His exploits at Wednesday have surprisingly handed him his first call-up to the Portugal senior squad, and he made his debut against Russia last week, capping off a superb start to the season.
Now, Everton are allegedly pursuing Joao, whose 6ft 3in frame and impressive athletic abilities make him an appealing target for the Toffees, as they search for a similar type of player to Lukaku in January.