It must be hastened for AS Roma to bring in Lukaku as soon as possible, because Juventus also has the same interest as the Belgian Bomber, due to the stricken crisis, so many injured players have made AS Roma need the figure of Lukaku to sharpen AS Roma's attack power, if not sooner then AS Roma will lose that opportunity to have Lukaku.
AS Roma are targetting two strikers, Azmoun and Lukaku and the Iranian striker even has been in Rome for final steps to sign with Roma but he has yet been a Roma player. The deal of Lukaku with Chelsea is far to completed even Roma staffs are in London to negotiate with Chelsea for a Lukaku loan transfer to Roma. Azmoun and Lukaku are different styles of striker and Azmoun is more adaptive to different tactics. Let's recall how Azmoun missed some opportunities in skirts of Leverkusen when they met Roma in Europa League semi finals in the last season. Perhaps, his performances in those matches are interesting enough for Roma to keep their eyes on the player.
And indeed at this time there are very strong rumors that Jose Mourinho is interested in bringing in Lukaku after the Belgian national player is no longer used by Chlesea, but that is with a loan option.
I think if this offer is seriously made by the Roma team then it will most likely be realized after Chelsea really don't want Lukaku anymore.
Lukaku will prioritize to play in Serie A than in other leagues as he does not fit with Premier League. Ligue 1 and Bundesliga are not his favorite leagues and La Liga likely does not fit with Lukaku style too.
In Italy, he betrayed Inter Milan and Juventus already stopped their interest on him. So the offer from Roma will be interesting for Lukaku as it is one of his best chances to leave Chelsea this summer. The barrier is his high salary and if Chelsea agrees to share it with Roma, the loan transfer will be executed. As with finance of Roma, they will surely not be ready to pay 100% salary of Lukaku.