The winger played 21 times from the start in Ligue 1 last season and featured in 16 Champions League matches as the French club won the double.
But his omission from the starting eleven for the Champions League final against Arsenal in Budapest proved a turning point.
PSG head coach Luis Enrique chose a forward line of Desire Doue, Ousmane Dembele and Khvicha Kvaratskhelia at Puskas Arena, with Barcola entering only in second-half stoppage time.
That decision convinced Barcola that a fresh challenge was necessary, and he has since made his desire to leave clear to the club, reports talkSPORT.
Across all competitions last season, Barcola contributed 13 goals and seven assists in 49 appearances.
PSG's official stance remains that Barcola is not for sale, and the club would prefer him to sign a new contract with two years left on his current deal.
However, PSG's position is likely to soften only if they bring in a suitable replacement for the left flank before sanctioning a departure.
Reports from Italy suggest PSG head coach Luis Enrique has identified Barcelona's Ferran Torres as the ideal candidate to fill that role, given their previous working relationship with the Spanish national team.
Barcola is currently with France's World Cup squad in North America, which means any definitive movement on his future is unlikely until after the tournament.
According to talkSPORT, Arsenal are among the leading candidates to sign Barcola, with manager Mikel Arteta keen to strengthen on the left side this summer.
The Gunners have already been linked with Club Brugge winger Christos Tzolis and Aston Villa's Morgan Rogers for that area, but Barcola's record at the highest level makes him a more expensive and more proven option than either.
Liverpool are equally alert to the situation, with manager Andoni Iraola looking to fill the gap left by Mohamed Salah's departure and reshape the attacking options available to him.
PSG's reported valuation of Barcola sits at around £60 million.
Beyond the Premier League, Bayern Munich, Barcelona, Real Madrid, Atletico Madrid, Inter Milan and Napoli have all been credited with monitoring Barcola's availability, underscoring the scale of interest that his performances have generated.
For now, the World Cup offers Barcola a platform to further demonstrate what he is capable of. Whatever he does in the tournament, the interest from England's biggest clubs will not be going away.