The 24-year-old scored 25 Premier League goals for Ronald Koeman's team last season, but the Belgian international seems set to call time on his Everton career - and there is no shortage of competition for his signature.
Lukaku, of course, moved to Everton on loan from Chelsea back in 2013 and it is a return to west London that is considered the most likely outcome for the striker this summer, with Betfair Sportsbook offering 8/15 (1.53) that the big Belgian joins the Blues for a second time.
With Diego Costa seemingly set to leave Chelsea this summer, Antonio Conte will certainly be seeking to strengthen his side's attacking options as the Blues bid to defend their Premier League title, while Chelsea are also chasing Champions League success this term, having sat out of European competition last season.
A return to Stamford Bridge for Lukaku may be a good fit for both parties, but the Belgian international is sure to have other options, with Manchester United also believed to be amongst his admirers.
Jose Mourinho, who was in charge of Chelsea when Lukaku left Stamford Bridge for Goodison Park, is believed to be keen on taking the striker to Old Trafford as United actively seek a replacement for Swedish striker Zlatan Ibrahimovic, who was freed by Mourinho's men last month.
There is 5/2 (3.50) that Mourinho and Lukaku are reunited in Manchester this summer - and that price could well be tempting for punters who believe that the Belgian will turn his back on the Blues.
Everton, of course, are desperate to retain Lukaku's services and 6/1 (7.0) is available that the 24-year-old remains an Everton player when the summer transfer window closes.
A move away from the Premier League may be appealing to Lukaku - should the 24-year-old decide to leave the English top flight, German champions Bayern Munich may be tempted to try to secure his services and the Bundesliga giants can be backed at 33/1 (34.0) to snap up the striker, while Paris Saint-Germain are available at 8/1 (9.0) to persuade Lukaku to move to Ligue 1.
A return to west London appears to be the most logical switch for Lukaku, though, and the skinny 8/15 (1.53) quote for Conte's charges to snap up the Belgian star are reflective of that.