The 27-year-old forward will be available on a Bosman and has been linked to both Premier League giants recently.
However, after starting just once for the Italian giants this season, Giovinco says that he will consider his future if his first-team opportunities do not improve.
"I'm not resigned [to being a substitute], it's not in my character," the Italy international told Rai Sport. "I have to evaluate many things but I'm not thinking about it now.
"I'll try to give my best, then we'll see later this year if I will continue at Juventus. I hope so.
"The season has only just begun. I hope to be able to add my contribution."
Giovinco started just six Serie A outings for the Bianconeri last season.