The 30-year-old faces a five-month first-team exile until January unless he can secure a Stamford Bridge exit route, and Roma are now preparing a loan offer as AC Milan monitor the situation.
Lukaku could be set for a reunion with former Chelsea manager Jose Mourinho, who briefly managed the striker during his second spell as Blues boss.
Chelsea want a substantial loan fee and the majority of Lukaku’s £325,000-a-week wages covered after failing to sell their striker this summer.
Roma have leapfrogged Juventus in the race, with the Turin club’s interest conditional on the sale of current striker Dusan Vlahovic, who is increasingly expected to stay due to his high wages and £68million asking price.
Chelsea earlier this summer turned down a swap deal including Lukaku, cash and Vlahovic.
Al-Hilal had previously agreed a deal at Chelsea’s £40million asking price but Lukaku refused the move. They have since signed Aleksandar Mitrovic from Fulham.
Chelsea are hopeful other Saudi Pro League options could become available later, with the league’s transfer window open until September 20.
The Blues have allocated Lukaku one of their two remaining international loan spots. New FIFA rules restrict clubs from sending more than seven players abroad every season and five have already been used. Deivid Washington, who joined in a £17million deal from Santos on Thursday, will likely take the sixth spot to join partner club RC Strasbourg.
Mauricio Pochettino is yet to speak to Lukaku since joining the club.