The 28-year-old forward, who recorded 15 goals and six assists in 39 appearances for Juventus last season, is leaving the Serie A giants after seven years with the club when his contract expires on June 30.
Inter Milan are believed to be the current frontrunners for Dybala's signature, but Tuttosport claims that talks between the Argentine and the Nerazzurri have been put on standby, as Simone Inzaghi is looking to offload some of his attackers to free up space in his squad.
Lautaro Martinez, Edin Dzeko, Alexis Sanchez, Joaquin Correa, Sebastiano Esposito, Andrea Pinamonti and Martin Satriano are all on the books at Inter, while Romelu Lukaku is set to return to the club on loan from Chelsea.
The report adds that Real Madrid are closely monitoring the situation and will consider a swoop for Dybala if they decide to sell Marco Asensio this summer.
Asensio, 26, has just a year remaining on his contract at the Santiago Bernabeu and has been linked with the likes of AC Milan and Liverpool.
The likes of Manchester United, Arsenal and Tottenham Hotspur have all allegedly turned down the chance to sign Dybala, while Jose Mourinho's Roma remain in the race for his signature.
CSKA Moscow 
FC Rostov 
Leicester 
Chelsea 
Valencia 
Betis 
Dynamo Kyiv 
Chornomorets Odesa 
Verona 
Inter 
Bayer Leverkusen 
FC Heidenheim 
Borussia Dortmund 
SC Freiburg 
VFL Wolfsburg 
Union Berlin 
Arsenal 
Nottingham Forest 
Everton 
Brentford 
Spartak Moscow 
Lokomotiv Moscow 
Rangers 
Dundee Utd 
Atletico Madrid 
Alaves 
Lens 
Marseille 
Ingulets Petrove 
Shakhtar Donetsk 
AC Milan 
Juventus 
ST Malo 
Bordeaux 
Manchester City 
Tottenham 
Eintracht Frankfurt 
Werder Bremen 
Girona 
Espanyol 
Feyenoord 
Heerenveen 
ST Etienne 
Montpellier 
Grenoble Foot 38 
Heart Of Midlothian 
Celtic 
Reims 
Lyon 
PSV 
Groningen 
Celta Vigo 
Barcelona 
Benfica 
Estrela Da Amadora 
Sparta Rotterdam 
AZ Alkmaar 
Southampton 
Liverpool