Reports from Italy claim that a fee has been agreed between the Serie A champions and last season's third-placed side, and Isla's agent Claudio Vagheggi claims that negotiations are at an advanced stage.
"We are discussing the contract details right now," Vagheggi told tuttomercatoweb.com.
"There was an interest shown by several important clubs to acquire the player, but I believe Udinese's excellent rapport with Juve influenced negotiations."
Chile international Isla alerted top clubs in Italy and beyond to his availability in February when, after suffering a season-ending knee injury, he announced he would be leaving the Stadio Friuli at the end of the season.
The 24-year-old had scored three goals and set up another two in his 21 Serie A appearances prior to that injury.