The Turin side are desperate to add a new left winger to their squad and head coach Antonio Conte considers the Peru international to be the perfect candidate
The Turin side have long been after a new left winger and have been linked with players such as Lyon's Michel Bastos, Real Madrid's Royston Drenthe and Sevilla's Diego Perotti in the past few weeks, but they have now apparently turned their attention to Vargas again.
The Fiorentina man has a contract with his current club until the summer of 2013 and the Artemio Franchi outfit are keen to hold on to the 27-year-old.
Nevertheless, Juve are hopeful that the inclusion of Amauri and Martinez will change their Serie A rivals' stance.
Amauri, 31, is no longer needed at the Turin giants following the arrival of Mirko Vucinic earlier this week, while the 28-year-old Martinez has been unable to make an impact since joining Juventus from Catania and is ready to move on again.
Juventus have yet to table an official offer for Vargas, but could make a formal approach for the wide-man in the coming days.