Lukaku, 21, hit 16 goals in 33 games during a loan spell with Everton last season, and made his move to Goodison Park a permanent one last summer, with the Toffees paying an alleged £28m to sign the then-Chelsea hitman.
Yet this season, the Belgian hasn't enjoyed the same success, scoring ten goals in 33 games, struggling to make the same impact for Roberto Martinez's underwhelming Everton side.
A top half finish appears to be the best that Everton can hope for right now, and speaking after their 1-0 defeat to Chelsea in midweek, Lukaku admitted his interest in moving on to a big club.
Now, rumours are swirling about Lukaku's future on Merseyside, with the Daily Mail claiming that Tottenham and West Ham are both looking to make summer bids for him.
Spurs may have discovered Harry Kane this season, but Mauricio Pochettino still needs another striker, given the continued struggles of Emmanuel Adebayor and Roberto Soldado.
Meanwhile, West Ham have just learned that Andy Carroll is out for the rest of the season, and may well be looking to add another striker at the end of the season if they have question marks over his long-term fitness.
If Lukaku wants to move to a bigger club than Everton, then Tottenham would be the sensible move, considering that Pochettino's men are battling for a Champions League place.
Despite West Ham's relative success this season, a move from Everton to Upton Park would be something of a sideways move - but given Lukaku's average performances this season and admission about wanting to play for a bigger club, his future is definitely a subject to keep an eye on in the coming months.