Catalan publication Mundo Deportivo says that the La Liga giants would be able to sign the Argentina international for a fee set in between €110m (£98.9m, $128.3m) and €120m - while other potential suitors would have to pay much more to lure him away from Juventus.
The 23-year-old forward has been linked with Lionel Messi's side since his early days at Palermo. Dybala finally joined Juventus in the summer of 2015 for around €32m but Barcelona reportedly revived their interest in the player last summer when Neymar's future at the club first came under scrutiny.
The Brazil international finally agreed a new deal last July at Barcelona and Dybala made the same decision in April, committing his long-term future to Juventus by putting pen to paper on a new contract until 2022.
However, recent reports have suggested that both sagas have been reignited after it emerged that Paris Saint Germain are considering meeting Neymar €222m release clause to lure him away from the Nou Camp.
Dybala meanwhile has emerged as the main option for Ernesto Valverde's new side to replace Neymar if the Brazilian finally makes the record move to the Ligue 1.
Mundo Deportivo is now providing a sensational update on the Argentinian's potential move to Barcelona after claiming that Dybala and his agent inserted an option in that deal signed with Juventus in April that allows him to leave Italy for the Catalans.
This option would allow Barcelona to sign him ahead of their rivals for a price set between €110m and €120m. Barcelona's rivals for his signature would have no such option.
According to the publication, Juventus agreed to set the price in accordance to the fee paid by Manchester United to sign Paul Pogba from the Serie A giants last summer.
Real Madrid and a host of Premier League clubs were also linked with Dybala before his contract renewal but Mundo Deportivo says that, if he leaves Juventus, it would be only be to join Barcelona and play alongside his compatriot Messi.
The report adds that the Catalans are yet to make any contact to complete his signing but would surely activate the option should Neymar finally join PSG.