Suso has been linked with a return to the Premier League and Gennaro Gattuso feels he deserves a contract extension at AC Milan.
Former Liverpool midfielder Suso, who is said to have a €40 million (£35m/$45m) release clause in his deal at San Siro, is reportedly a target for Tottenham and Arsenal.
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The 25-year-old has been a key part of Gattuso's squad this season, featuring in all but one of their 23 Serie A matches and contributing five goals and eight assists.
Suso is under contract at Milan until June 2022 but Gattuso believes he has done enough to warrant fresh terms being offered.
"My job is to coach, I am not an agent or a sports director. He deserves a contract renewal, but it depends on the management," he said of Suso.
"There is great respect for Suso and he is contributing a lot to the team.
"He immediately made himself available after coming back from a leg injury [in January]."
Suso has previously stated a desire to remain at San Siro.
Having starred for Milan in the 2017-18 campaign, rumours regarding a move elsewhere began to surface.
The man at the centre of such talk was fully aware of the speculation surrounding him.
He was, however, eager to point out that he remains fully committed to Milan.
Suso told Tuttosport last summer: "I think I've always said that I'm very happy here.
"I'm very settled and there's nothing to make me think that I have to leave.
"If the club want to grow with me, I'll be happy, because Milan is my home now. If that was not the case, if it was a year of transition instead of growing, I would have said so."