Giaccherini arrived at the Stadium of Light on a four-year deal from Italian champions Juventus in the close-season, but the attacking midfielder has endured an indifferent debut campaign In England, making just 16 Premier League starts.
With Sunderland's top-flight status hanging by a thread, reports have suggested Giaccherini could cut short his stay on Wearside, with Serie A duo Fiorentina and Genoa reportedly ready to offer the 28-year-old an escape route.
However, Poyet believes it is soon to discuss the Italy international's future, especially with the season yet to reach a conclusion.
"It's too soon to be talking about that (Giaccherini's future) because nobody knows really," he told The Hartlepool Mail.
"I'm surprised they're talking about it so early, because the season isn't finished."
Giaccherini has become increasingly isolated from Sunderland's first-team plans, making just one Premier League start since New Year's Day, and was not even among the substitutes in the club's last two top-flight fixtures, which resulted in defeats to West Ham and Tottenham.
Explaining Giaccherini's omission, Poyet added: "When I planned the team (for West Ham and Spurs) I changed the bench a little bit.
"Normally, I would always put on a couple of strikers, couple of midfielders, a full-back and a centre-back - depending on the shape.
"But I think it's time to take a risk. We're trying to make the bench in a certain way and sometimes we have three strikers on there."
