Alisson has been frequently linked with a transfer to Anfield, but Monchi has insisted that the Serie A giants received no bids during the first month of 2018.
At the presentation of new signing Jonathan Silva, Monchi said: "Did any offers come in for Alisson? No.
"It's too early to talk about the next transfer window, it's not very useful talking today, February 1, about who will stay or go."
Alisson has previously claimed that he may consider his future at the Stadio Olimpico during the summer.