Di Maria joined PSG from Manchester United in 2015 but is to leave the French capital at the expiration of his deal at the end of June.
Juve has reportedly offered Di Maria a one-year contract with the option of an additional one-season extension.
Reports suggest Di Maria is intent on staying in European football for just one more season, though, before playing at the 2022 World Cup in Qatar and returning to compete in his native Argentina.
That is said to have led to a delay in negotiations between the 34 year-old and Juventus.
Former Juve goalkeeper Buffon encouraged the Bianconeri to push the deal through for Di Maria, with the Italy legend suggesting he would be as influential in Serie A as the late, great Maradona was with Napoli.
"Di Maria in Serie A is like Maradona," Buffon told La Gazzetta dello Sport. "Footballers must be valued considering where they play. Serie A, today, is technically poorer and Angel has so much technique.
"He is decisive in front of goal, he dribbles past his opponents. He is good at making assists and runs up and down on the pitch. He can play in different roles."
Buffon is speaking from experience, having crossed paths with Di Maria at PSG in the 2018-2019 campaign.
The Parma goalkeeper also suggested Di Maria is talented enough that age should not be a factor as Juve aim to secure the winger.
"I am 44, but I still play, age doesn't matter. Motivation and passion are more important and so is determination," he added. "If Di Maria joins Juventus, it means that he's ready to do so.
"He is an exemplary professional, one who never gives up and fights during games and training sessions. For today's Serie A, he'd be like Maradona.
"At PSG, I played with Neymar, a young Kylian Mbappe, Marco Verratti… but Di Maria was not inferior to no one.
"When he won the Decima [the 10th Champions League title] at [Real] Madrid in 2014, he was playing with Karim Benzema, Cristiano Ronaldo, Luka Modric and Toni Kroos.
"He was always a step back from them but knew how to play as a winger, attacking midfielder and even 'Mezzala' [a wide central midfielder in a diamond or three-man midfield].
"Whoever signs him, and I hope it's Juve, it will be a good deal. We are talking about a champion."