The Premier League champions refuse to pay the full fee Everton are demanding, but it is thought Lukaku has agreed with his agent to prioritise a return to Stamford Bridge over a move to Manchester United.
Chelsea are willing to hold out for a better deal, but one is not imminent despite the 24-year-old declaring that he had made a decision over his future.
They are keeping the lines of enquiry open with Alvaro Morata, who Antonio Conte rates very highly. The Real Madrid striker has drawn serious interest from United and AC Milan and could leave the Champions League winners in search of more first team opportunities.
The Blues have been working for months to find a replacement for Costa, who was told by Antonio Conte that he was no longer needed, and have made Lukaku their top target.
The Spain international has had two possible destinations ruled out as Atletico Madrid serve their ban transfer ban and Tianjin Quanjian, along with the rest of the Chinese Super League, were burdened with a 100% tax on transfers by the authorities. However, Milan are also said to be interested.