The 27-year-old Italian international has been linked with a move away from the Serie A champions after falling down the pecking order in Turin.
However, Giovinco is eager to remain with Juve during the January transfer window and fight for his place in the team under Massimiliano Allegri.
"I have to evaluate many things but I'm not thinking about [leaving] now," he told Rai Sport. "I'll try to give my best, then we'll see later this year if I will continue at Juventus. I hope so."
Juventus continue the defence of their Serie A title on Saturday when they travel to Sassuolo.