The 20-year-old - who is currently on loan at Everton - has enjoyed a great season at Goodison Park having already scored 12 Premier League goals this term.
Recent reports have suggested that Chelsea boss Jose Mourinho is ready to let the Belgian international depart Stamford Bridge in the next window.
And, if reports are to be believed, Arsenal boss Arsene Wenger is interested in a summer swoop for the Blues forward.
The Arsenal manager wants to bring a new forward to the club, with Olivier Giroud currently acting as his No.1 striker.
However, with recent reports having indicated that Arsenal's Premier League rivals Tottenham and Everton are in the race for the player's signature, it remains to be seen as to which club Lukaku will opt for in the next window.
For now though, Lukaku will be gearing himself up to play against Arsenal this weekend as Everton host the Gunners on Sunday afternoon. Both sides will be desperate to gain all three points as the race for Champions League qualification continues.
Meanwhile, Lukaku's parent club Chelsea are also involved in action this weekend as they host Stoke City at Stamford Bridge.