The Ivorian has given his former club a chance to have an improved season in Europe
The French giants are away at Borussia Dortmund for the Round of 16, first leg match on Tuesday as they press for their first ever Champions League crown.
Having assembled a star-studded squad in recent seasons, PSG have always been heavily-tipped for European glory.
Their last three campaigns have ended in the Round of 16 including last season where they were eliminated by Manchester United, having started this stage with a 2-0 away victory before United turned the tables in Paris with a 3-1 victory.
“This year, I think Paris have resolved certain problems. Frankly, they are likely to go far because there is less pressure on them this season. If Paris want to win the Champions League soon, don’t put pressure on them,” Aurier told France Football.
“Last season, who could have imagined that Manchester United would pass [through PSG in the Round of 16]? I could have bet with my house that Paris were going to win. It was unimaginable. There, it has to be the opposite: that nobody is counting on the Parisians this year [for them] to get to the end.”
Aurier joined Tottenham in August 2017 after spending three seasons at PSG.