Giaccherini has been linked with a return to his homeland throughout the campaign, despite only joining Sunderland from Serie A champions Juventus in August.
Italian sides Fiorentina and Genoa have been credited with an interest in Giaccherini, but the 29-year-old Italy international told TuttoJuve.com that he wants to remain at the Stadium of Light after coach Gus Poyet preserved Sunderland's top-flight status.
"It's still early for me to be thinking about my future," said Giaccherini, who scored four goals in 24 appearances as Sunderland avoided relegation by five points.
"I am on holiday but my intention is definitely to remain at Sunderland.
"I am happy at the club and when it is the right time I will talk to the boss in order to hear his thoughts on my role.
"I have three years of contract and I want to remain in the Premier League, wearing this shirt."
Giaccherini was a high-profile signing at the start of the season, joining Sunderland on a four-year deal during Paolo Di Canio's brief tenure in charge.
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