The 29-year-old has been linked with a return to his homeland throughout the campaign, despite only joining Sunderland from Serie A champions Juventus in August.
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"It's still early for me to be thinking about my future," Giaccherini, who scored four goals in 24 appearances as Sunderland avoided relegation by five points, told TuttoJuve.com.
"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.