The Stamford Bridge club are reportedly willing to offer £70 million for the 23-year-old striker but are wary of Everton's concerns over next season's squad.
With that in mind, Italian boss Antonio Conte is readying himself to allow second-choice forward Remy to leave the club in order to persuade the Merseysiders to depart with their main goal threat.
Per Phil Kirkbride of the Liverpool Echo, Chelsea are now convinced of breaking Everton's resolve and bringing the former Anderlecht attacker back to west London.
Daily Mail journalist Ell Bretland feels the offer including Remy would be good business for Everton:
Kirkbride reports Chelsea had a clause inserted into Lukaku's contract when they sold the player to Everton in 2014 giving them first refusal on any sale offer. Ronald Koeman remains intent on keeping hold of his prized asset and turned down a £57 million offer from Conte's side this week, per Kirkbride. However, the Blues will push on with their pursuit and are expected to return with an improved bid.
Andre Villas-Boas signed Lukaku in 2011, but he failed to make regular first-team appearances before being sent out on loan to West Brom and then ultimately dumped by then-manager Jose Mourinho. However, with Lukaku harbouring ambitions of playing UEFA Champions League football, a return to his former club now looks on the cards.
Per Allan Velante of Sky Sports, he was quoted as saying in March: "That is the next step for me. I'm 23 next summer, and I think it would be nice to play in the Champions League from next season."
Lukaku's displays during the 2015-16 season were his most complete and productive since his arrival in English football. Per WhoScored.com, the powerful attacker netted 18 Premier League goals in 37 matches while also providing six assists.
In contrast, Remy was handed the opportunity to show his worth in just 285 minutes of league football last year, scoring one goal in the process, per WhoScored.com. In spite of his recent link to Everton, Besiktas' interest in the France international has not diminished, according to Turkish-football.com:
Elsewhere, Oscar's time at Chelsea appears to be drawing to an end with Conte willing to sell the attacking midfielder, per the Sun (h/t Chris Davie of Goal).
The Italian tactician has been unimpressed by the Brazil international's work rate and is prepared to accept offers of £30 million for the former Sao Paulo playmaker, with Serie A outfit Inter reportedly keen on the 24-year-old.