Suso is in talks to extend his Milan contract to June 2021 and more than double his wages, according to the latest reports.
The winger arrived for a nominal fee from Liverpool in January 2015, costing just €1.3m.
He has been a key figure this season, scoring six goals with seven assists in 25 Serie A appearances.
His current contract holds him to San Siro until June 2019, earning just €1m per year.
According to Sky Sport Italia, Milan’s new Chinese owners are laying the groundwork to offer a new deal to June 2021.
The 23-year-old would more than double his wages to €2.5m per year.
Any deal would not be confirmed until after the closing of the takeover, which is set for March 3.