The 36-year-old Italy forward, whose current deal is set to expire in the summer, has netted four times in 22 Serie A appearances for Juve this season.
“The door for his contract renewal is always open,” Juventus general director Giuseppe Marotta told Gazzetta dello Sport. “We hope we will arrive at an understanding as soon as possible so that he will continue with us.
“We would like to see Del Piero step onto the pitch of our new stadium, which we will play in next season.”
Reports in the Italian media suggest Del Piero could sign the extension as early as this week – and the striker understood to be ready to take a pay-cut to stay with the Serie A side.
Del Piero joined Juventus from Padova as an 18-year-old in 1993 and has scored 280 goals in 666 appearances for the Italian side.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news