Having long been the dominant force in French domestic football, European supremacy has eluded the capital club.
The 2011 takeover of the club by Qatar Sports Investments took PSG to another level financially, paving the way for Neymar's arrival six years later.
But even with that backing and a wealth of talent on the pitch, the most sought-after prize has eluded the Parisians.
Asked if that could change in 2020, when the first hurdle for Thomas Tuchel's side is to get past Borussia Dortmund in the round of 16, Neymar said: "Yes, I think there's a possibility we can make it.
"In terms of the team and players, since I've played for PSG, this is the most prepared and strongest year we had in my opinion. So, I think we have a chance.
"Although PSG has never won the Champions League, we are going to fight for this title. We know our values and we hope to be in the final."
Neymar, who won Europe's top prize with Barcelona in 2015, has endured a sometimes troubled relationship with the fans at PSG, with reports over his apparent desire to leave doing little to endear him to the faithful.
Injury niggles have also limited his playing time, with off-field issues placing further strain on the 27-year-old.
The former Barcelona star concedes the past 12 months have been "tough", but he hopes to learn from his experiences.
"Professionally and personally, 2019 was a tough year for me," he said.
"It was a year full of learnings and turnarounds. I injured myself and had to come back. Then I injured myself again.
"Although it seems like a bad year, it was a year full of learnings and lots of experiences. I am taking the positive side of it so that 2020 can be better."