Silva has been Benfica's top target for a while to replace the Portuguese tactician, and there were even rumours that the Fulham manager had signed a two-year contract with the Eagles.
The 48-year-old remains in charge of the Cottagers, at least for the time being, and, according to Sky Sports, he is set to hold talks with the Premier League side about his future this week, as his contract expires next month.
Should he decide to leave West London after five years, Benfica are the frontrunners to land his signature, with former Manchester United boss Ruben Amorim also on their radar.
Silva enjoyed another productive campaign at Fulham, as they finished 11th in the top flight following a final-day victory over Newcastle United.
The Cottagers have already offered their Portuguese boss a "lucrative contract", too, and it has been on the table for quite some time, so perhaps he is edging towards the exit door.