Dest, 23, has been a mainstay in the PSV side this season as they won the Eredivisie, with coach Peter Bosz recently expressing a desire to keep him beyond the summer.
However, with Dest now facing months out of action, he will instead formally return to his parent club Barcelona from July to carry out his rehabilitation.
PSV signed Dest on a season-long loan last year in a deal which included an option for them to make the move permanent this summer for €11 million.
Dest made 36 appearances for the Dutch champions in all competitions before getting injured in training on April 20.
The full-back confirmed last week that he had torn his ACL and would need an operation, ruling him out of the Copa America this summer with the United States.
Sources add that PSV may revisit the situation when Dest is fit again, although he is unlikely to feature again in what remains of the calendar year.
Dest's contract with Barca expires in 2025, so he could potentially leave the Catalan club as a free agent next summer if he does not move on before then.
After breaking through at Ajax, Dest joined Barca in 2020 for a fee of around €20 million, featuring regularly in his first season under coach Ronald Koeman.
In total, he has made 72 appearances for Barca, but he has spent the past two campaigns out on loan, first with Italian side AC Milan and then with PSV this term.