It's been claimed Jurgen Klopp's side are close completing the signing of Carvalho for an initial fee of £5million, which could rise to over £7.5m, having continued to negotiate behind the scenes.
But Silva says: "It has been a rumour since November, probably. I am speaking every single week about Fabio Carvalho. His full focus is on our club.
"I can't lie to you, we have been trying to renew his contract and it has been really difficult for us.
"Unfortunately the player has got into the last year of his contract and is a player who is doing a fantastic season. I really love him as a football player and we are helping him to grow as a man and football player.
"About his future, I hope I can have a right answer for you soon - probably the end of the season. It has been tough for us to renew his contract, but let's see what we can do."