The move would come alongside another departure from the club, with striker Rory Wilson also being lined up for a fresh loan move to Sweden.
The Serie A club are prepared to make an initial offer of about £6million for Martinez, plus performance-related bonuses.
The goalkeeper's advisors had agreed terms with Juventus intermediaries earlier in the summer, and if the Argentina international completes his move to Turin, he can expect to earn about £200,000 a week, a significant rise on his current deal at Villa Park, which sits around the £130,000-a-week mark.
Aston Villa are confident of replacing Martinez with Parma goalkeeper Zion Suzuki, who is likely to cost up to £30million but would earn substantially less than his predecessor. Should the deal go through, Villa will have sold three of their top earners this summer in Martinez, Youri Tielemans and Lucas Digne.
The Suzuki side of the deal has already had a turbulent few days, having briefly appeared to collapse over agent commission disputes before Villa renewed their pursuit of the Japan international.
Villa's academy business is also active elsewhere, with Swedish clubs IK Sirius and IFK Goteborg both showing interest in taking forward Rory Wilson on loan. The Scotland Under-21 international, who has yet to make a senior competitive appearance for Villa, spent the spring on loan at Austrian side Sturm Graz, making four appearances before returning to Villa Park this summer.
According to Expressen, Halmstads BK have also attempted to take Wilson on loan, while the Swedish paper reports he has additionally been linked with Malmo FF. Halmstad are understood to have made an ambitious offer, though Wilson is said to be attracting interest from clubs in other leagues too, with Swedish journalist Luca Bendoni previously reporting that IF Elfsborg have also shown interest in the striker.
The 20-year-old joined Villa's academy from Rangers in 2022 and has continued to be linked with loan interest from across Europe as the club looks to find him regular first-team football away from Villa Park.