The Turkish club are working on a deal worth €8million net per season, with add-ons that could bring in a further €1.5million for reaching 20 appearances, another €1.5million for 15 goals, and €1million should Fenerbahce win the Turkish title.
On the Milan side, the Istanbul club value Leao's contract at around €40million, a figure that could rise to €50million with bonuses included, and are only interested in a permanent transfer rather than a loan.
Jorge Mendes, Leao's agent, is understood to be working behind the scenes to build the conditions for a formal proposal to Milan, though Fenerbahce must first trim their squad given restrictions on the number of foreign players they can register.
According to Gazzetta dello Sport, Leao himself has shown openness to the move, though Milan continue to regard him as part of their squad and have no intention of easing his departure without an offer they consider adequate.
Leao addressed the speculation directly during a lengthy appearance on the Brazilian podcast Podpah, confirming he had discussed the possibility of a new challenge with the club but stopping well short of declaring his Milan career over.
"I'd already spoken with the club about the possibility of trying a new experience, I don't know if it will happen," he said.
"I have to report back on the 29th and for as long as I'm there I'll give my maximum, always with respect for the shirt that has given me everything.
"I think it's a club that has helped me a lot in every aspect, but in life you have ambitions for other things too, and if it happens, I'll look at the options. For now I remain a Milan player."
The forward also touched on a possible future in Brazil, name-checking Corinthians after training with the club during the off-season.
"One day, yes, maybe, because I identify a lot with the culture, with the people, with the climate. Not Sao Paulo... which is cold. And in Rio there's only one club I'd like to play for, there's only one in Rio... But I really liked Corinthians, the people there were very kind to me, the facilities were excellent.
"I'm training to go back for pre-season and I've also let Milan know, so as not to create any friction. Corinthians, thank you very much, we're together. You never know, you never know what the future holds - I'm already grateful they opened their doors for me to train."