The Parc des Princes side have already secured the services of high-profile names such as Jeremy Menez, Javier Pastore and Kevin Gameiro this summer, and Leonardo feels that they can make an impact in Europe in the near future thanks to QSI's financial backing.
"I really believe that one day PSG can finish in the first position of the Champions League," Leonardo was quoted as saying by the BBC.
"I played here at the highest level 14 years ago, and I lived the best moments in the history of the club. We played in Europe at the highest level with very good players. PSG have to come back to that level, even inside the club, to have that winning mentality and to start the season thinking we can win the title and not just to participate.
"The Champions League is very important but it will not kill us if we're not in it next year. We have a programme, but it's impossible to programme the results and the players' performance."
Paris Saint-Germain currently sit fifth in the Ligue 1 table with nine points from four games.
They started the Europa League group phase with a 3-1 win over Red Bull Salzburg on Thursday.