The central midfielder has spent the past 18 months with Monaco on loan.
He wanted to sign permanently, but Monaco did not have the funds to make the move happen.
Now Sampdoria are in a prime position to secure Silva, per Leicestershire Live.
The Portugal international has not enjoyed a good career at Leicester, and wants to move on.
He has a year left on his contract, which he signed when he arrived from Sporting CP in 2017.