The 23-year-old just extended his contract with Juve until 2022 in April and Alves believes Dybala will struggle to achieve his potential if he stays with Juventus.
The Brazilian full-back joined Juventus just a year ago and helped his team to clinch a domestic double with Serie A and Coppa Italia title.
The defender was even the main lynchpin to inspire his team to take them into Champions League final where they lost to mighty Real Madrid to 4-1.
However, the recent fan favourite might now face the wrath of the Juventus fans and hierarchy with his staggering comments on his team-mate Paulo Dybala.
"We have talked and I told him that one day he will have to leave to improve," Alves told Brazilian television channel Esporte Interativo.
"He is a jewel that will blossom. We talked so many times about it and I said one day, I don't know when, that he will have to leave Juventus if he is to improve even more."
The Brazilian defender also admitted that one day he also would like to play in England and he is now keeping all his options open.
"Last year I turned down many offers from the Premier League because I felt I had to go to Serie A," he told Esporte Interativo.
"There is a great defensive culture, and to go and play in England you have to know how to defend well. I hope that one day I will go there. Who knows? We'll see."
Alves has now only one year remaining on his contract but with clubs like Tottenham Hotspur and Chelsea chasing the player, there is a big possibility that he could join them in the upcoming Summer.