Former Italian coach Marcello Lippi is reported to have wanted him in China, where he is boss of champions Guangzhou Evergrande.
But Furio Valcareggi has told Radio Kiss Kiss that Giaccherini is staying on Wearside, despite interest from China.
"Marcello Lippi tried to take Giaccherini to China, we thank him but Emanuele doesn't leave Sunderland," he said.
"The Premier League's table is very tight and there is plenty of time to return to even a European position."
Valcareggi also said that Parma and Genoa had shown an interest in Giaccherini.
"Pietro Leonardi [Parma's general director] contacted me because they like the player and they seek a replacement for Jonathan Biabiany," he said.
"Genoa made an attempt for Emanuele too, but I repeat that he remains at Sunderland also because he has a major contract with them and we want to respect it."
Meanwhile, Modibo Diakite remains on the agenda of a number of Italian clubs, and Sunderland boss Gus Poyet has already said he would not stand in the way of the former Lazio defender - should he find a move.
His agent Ulisse Savini told Tuttomercatoweb: "Modibo could return to Italy in this January transfer window, there is a 50 per cent chance.
"Parma and Chievo are interested in him. But it is possible even he could remain in the Premier League, we are evaluating various options."