Genoa president Enrico Preziosi has declared an interest in signing Suso on a permanent basis from Serie A rivals AC Milan for a fee of €10 million.
The 22-year-old attacking midfielder linked up with the Rossoblu on a six-month loan during the January transfer window after limited opportunities at the San Siro.
Suso has featured regularly for Gian Piero Gasperini's side in the months that followed and he scored his first hat-trick for the Liguria outfit in a 4-0 win over Frosinone earlier this month.
The Spaniard, who spent five years with Liverpool before joining the Rossoneri in 2015, is expected to return to his parent club at the end of the season, but Preziosi has another plan in mind for Suso.
"He wanted Genoa just for six months, while I wanted him for 18," Preziosi told Il Secolo XIX. "Now I'm willing to negotiate the option to buy with [Adriano] Galliani, even for €10m."
Genoa are just nine points behind sixth-placed Milan in the league standings and will be searching for a third straight win when they travel to struggling Carpi on Saturday.