AC Milan wanted the Spaniard on a long-term loan deal and made a formal offer for the 20-year-old in the summer transfer window but advances were rejected by Brendan Rodgers.
However, Milan chief executive Adriano Galliani has remained desperate to bring Suso to the San Siro, who’s contract expires at the end of the current season.
He said: “Transfer market? I know where can improve, but I don’t tell that to you.
“Suso? He has an expiring contract and he’ll tell us if he wants to move or stay.”
Suso has played just 21 times for Liverpool since signing for the Anfield club from Cadiz in 2010.
By Ollie Carroll
Twitter: @Ollie_Carroll_