The Turin giants are keen to add some more depth to their attack and they see the 23-year-old Pereyra as a useful addition to their squad, having captured €20 million (£15.8m) striker Alvaro Morata earlier in July.
"Pereyra is in Turin for Juventus medical," read a statement on the club's official website.
"The 23-year-old midfielder is currently undergoing medical tests ahead of a proposed move from Udinese.
"The young Argentine will take his first tests at the city's Clinica Fornaca di Sessant, before completing the procedure at the Istituto di Medicina dello Sport medical centre."
Visite mediche in corso per Roberto Pereyra pic.twitter.com/QImUHJ9SsW— JuventusFC (@juventusfc) July 23, 2014
The Argentine has since developed into an important first-team member at the Stadio Friuli, making over 100 official appearances in the past three seasons.
Juventus have already secured the services of Morata from Real Madrid, Patrice Evra from Manchester United and Kingsley Coman from Paris Saint-Germain as new head coach Massimiliano Allegri looks to bolster his squad to challenge for both domestic and European honours next season.