Argentina forward Dybala starred alongside Pogba for a single season before the midfielder departed the Bianconeri to return to Manchester United in 2016.
Pogba has repeatedly been linked with a second move away from Old Trafford in recent seasons, however.
Real Madrid has been hotly tipped to bid for the World Cup winner, yet former club Juve are also said to be in the running.
Dybala would appear keen for such a transfer to materialise, as he highlighted his positive relationship with Pogba as he showed off a collection of matchworn shirts on UEFA.com.
"I couldn't overlook a shirt like this, of course," Dybala said, referring to a United shirt from Juve's 1-0 Champions League win in Manchester in 2018.
"It's from Manchester, from my friend Paul, whom I admire as a person even more than as a football player.
"I had the chance to share great things with him and hopefully I can repeat that someday."
Dybala scored Juve's winner at Old Trafford and added: "To score and to win a game in that way makes it even sweeter, and to be able to swap shirts with your friend is one of the most beautiful things you can do in football."
The possibility of Dybala following Pogba to United was mooted last year as the Bianconeri preferred to build around former Old Trafford favourite Cristiano Ronaldo.
But Juve sporting director Fabio Paratici last week told Sky Sport Italia the club wanted Dybala to "stay with us for as long as possible" as they target a contract renewal.