Spanish publication 'Mundo Deportivo' reports that the Catalans decided to pull out of the move, which was already starting to come together, as they didn't believe that it was in the best interests of Lionel Messi.
The same source claims that Barca eventually wound up rejecting the chance to sign the former Palermo star due to fears of his incompatibility with Messi on the pitch.
The pair are international team-mates and whilst they are thought to get on well with each other, with Dybala admitting to being a huge fan of Messi's, there are fears that the pair do not combine well on the pitch as they both like to operate in the same areas.
This was alluded to by Argentina boss Jorge Sampaoli ahead of the game against Peru on Thursday, when he explained that he would not put the duo on the pitch together as they need time to work on their partnership play.
"As there is no time to work the Dybala-Messi relationship, we should go to something more concrete," he told the press.
"Leo needs to move in the field normally as he does with his club," Sampaoli continued. "To invent a position or to structure him, that would be crazy.
"When we use the 4-2-3-1 formation, he is even further forward, always near the box. Being away from the box puts our best player far from the scoring positions and that is what he does best in his club.
"It is my job to make him understand that he is vital in the finishing, in the last third of the pitch."
When forced to choose between the two Sampaoli obviously opted for Messi, following Barcelona's lead.
Can the pair form a devastating partnership in the future for club and country?