The 30-year-old wants to leave Stamford Bridge and has not spoken with Chelsea head coach Mauricio Pochettino since his appointment on July 1.
Chelsea would prefer to let Lukaku leave but the Belgium striker rejected a proposal to join Saudi Pro League club Al Hilal and flirted with a move to Juventus while Inter Milan had two bids rejected.
Inter withdrew their interest following a fan backlash but sources have told ESPN that Lukaku is now reluctant to join Juventus after becoming frustrated at the amount of time it has taken the club to negotiate a deal with Chelsea.
Instead, Lukaku is now focused on joining Roma if possible. Given just one week of the transfer window remains, sources have told ESPN that Chelsea are now willing to sanction a loan deal but will seek a significant fee and demand that his prospective new club take on the bulk of his wage, which is around £300,000-a-week.
Speaking on Thursday about Lukaku, Pochettino said: "If the player and clubs wish is to find a solution, it's not me, it's them. In that case, the player and the club will meet and inform to me that things changed. I'm not going to move until the club or the player want to talk with me.
"I am here, I accept the situation that was here when I arrived. Club and the player, both try to find a solution. The future can change things."