I don't think Mourinho has a desire to sign Lukaku for Fenerbahçe. Because he already stated clearly that he didn't want Lukaku and Dybala unlike the rumours. Therefore I don't expect Fenerbahçe to sign any of them.
The current more probable options for him are said to be Milan, Napoli and Saudi Arabia teams. If Napoli manages to keep Osimhen for another year then I don't think they would go for Lukaku. But when it comes to Milan I think they would be interested just as they were in the past. Because Giroud is leaving in July. The only natural striker left in the squad is Jovic after that.
But while there is an option like making a lot of money in Saudi Arabia maybe Lukaku would rather consider that option.
But it is reported that Napoli's new coach, Conte, is very interested in bringing in Lukaku. It is even reported that Conte has approached Lukaku since Conte officially became Napoli coach. And it seems that Conte has also been given quite a lot of authority when it comes to player transfers at Napoli. So if Conte is really sure about his choice then he will definitely try to get it.
I also don't think Mourinho will take Lukaku to the new club he trains, namely Fenerbahce. Even though Mourinho has a good relationship with Lukaku. But that doesn't mean he will always want Lukaku in the team he coaches.
Yea, it's actually true that jose Mourinho don't want Romelu lukaku at fernabache, because I don't think they have the financial power to pull through such a deal, and besides I don't think Romelu lukaku would want to go to turkey, even if it's just for a season, so it's more likely not to happen, even though their was an intent from jose Mourinho.
The club that I think that has the greater chance of signing Romelu lukaku is Napoli, because of Antonio conte, which is the new head coach of Napoli, and another advantage he has is that since he was the one that brought the best out of Romelu lukaku at inter Milan, lukaku would likely favour a move to Napoli more than any other club, though it's still early days in the transfer window, let's just look how this particular transfer would saga plays out.