Reports in the Italian media suggest the Black Cats have made a bid of around £6.8m for the Italy international, with extra fees to be paid based on appearances and goals.
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"Giaccherini was valued, they offered him an important contract,” the Bianconeri boss revealed at a press conference. “I'm happy for him but unhappy for me.
“I'm not happy with the sale of Giaccherini but in times of crisis when you buy must also make sacrifices.”
The winger has been in and out of the first team since moving to Turin from Siena two years ago, but featured in every one of his country’s Confederations Cup matches this summer.
Paolo Di Canio’s men are thought to have offered Giaccherini double his current wages in order to tempt him to the Stadium of Light, having already signed seven players in a busy transfer window.