Milan have turned down a €7m offer from Celta Vigo for Suso, but would be tempted to sell for €10m.
According to La Gazzetta dello Sport, a proposal was sent to San Siro by the Spanish club.
Celta Vigo directors were impressed by Suso during Wednesday’s Trofeo TIM, which saw them face Milan and Sassuolo at the Mapei Stadium.
The 22-year-old’s agent Fabrizio De Vecchi was also present at the event.
So far the Rossoneri have slammed the door, but could be prepared to listen if the offer was raised to €10m.
Above all, Suso would be surplus to requirements if Milan manage to get Juan Cuadrado on loan from Chelsea.
Suso arrived from Liverpool for just €1.3m in January 2015, but barely featured in a Milan jersey.
He did very well during a six-month loan spell at Genoa, scoring six goals with two assists in 19 Serie A games.