Giaccherini arrived at the Stadium of Light on a four-year deal from Italian champions Juventus in the summer but has endured an indifferent debut campaign, 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 at the end of this season, with Serie A duo Fiorentina and Genoa reportedly ready to offer the 28-year-old an escape route.
|4/1||Sunderland are 4/1 with Bet365 to stay up this season|
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."