The 32-year-old is a free agent next month when his contract with Premier League side Arsenal expires.
Gallas has spent the past nearly a decade in England after joining The Gunners in 2006 after five years with Chelsea.
The defender's agent Etienne Mendy has been in touch with Juve's officials and hopes to finalise a deal in the coming days.
"I can confirm Gallas' interest in Juventus," Mendy told itasportpress.
"As soon I return to Europe I'll meet Juventus' leaders to find a financial agreement after making first contact a few days ago.
"Juventus want Gallas and William would be happy to wear the Bianconeri jersey."
Meanwhile, Juventus could make it a double signing after Catania managing director Pietro Lo Monaco confirmed Jorge Martinez will leave.
Martinez is set to sign for Juve on Wednesday, a deal that the Catania official insists will be the club's last departure this summer.
"(Jorge) Martinez will go to Juventus, there are no doubts," he told Sky Italia. "The agreement was reached, the player is expected (on Wednesday) in Italy to sign.
"He's an important player that will play in a great team. With the departure of Martinez, we closed the transfers out. We want to keep all our jewellery. Next season we want to have a good season."