Liverpool reportedly want to bring the Spaniard, who left the Merseyside giants for the Rossoneri in 2015, back to Anfield in the winter transfer window.
Suso joined Liverpool from Cadiz in 2010 but was unable to break into their first team on a regular basis.
However according to the same source, Suso seems unwilling to return to Anfield, as he is already doing great in Milan.
The Italian club said: "With Suso, Milan was very clear in the summer: we do not even give in for an offer of 80m euros".
The forward took to his personal Instagram account to downplay speculation over his future at San Siro amidst talk that former club Liverpool are plotting an extraordinary transfer for him.
"That was how the outstanding Spaniard was convinced in September to sign a new contract in what was a very important operation for Milan. All the other players mentioned today from Biglia to Kalinic to Locatelli will remain".
The 24-year-old also made his senior debut for Spain last November, featuring in the 3-3 friendly draw with Russia.
Ben Gladwell reports on Serie A, the Italian national team and the Bundesliga for ESPN FC, UEFA and the Press Association.
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