The 30-year-old winger, who signed for £6.5m two seasons ago under compatriot Paolo Di Canio, continued his recovery from injury as he starred for Dick Advocaat’s men in a friendly win over Darlington on Thursday.
The Italian made just eight Premier League appearances for the Black Cats last season after struggling with a groin and ankle injuries.
Having struggled to make an impact at the Stadium of Light, Giaccherini had been linked with a return to Italy, but he retains a desire to stay at the club, according to his agent Furio Valcareggi.
He told Italian outlet Tuttomercatoweb: “He remains with Sunderland, he had two serious injuries last season.
“He wants to redeem himself with his club, he is happy to stay.”