The 28-year-old made 16 starts for the Black Cats following his move from Juventus last summer, but he fell from favour and was last named in Gus Poyet's starting XI against Liverpool on 26 March.
The Italy international was one of a host of signings made by Paolo Di Canio, Poyet's predecessor in the Sunderland hotseat, but since the start of this year he has been mainly used as a substitute by the Uruguayan during the club's successful fight against relegation.
"I would like to play again here in the Premier League. I want to stay and do even better with the experience I have accumulated," declared Giaccherini, who scored four goals last season.
"I still have three years of contract. I'm fine here, but do not know what will happen. I will speak with Poyet and we will see."