PSG have been the most successful club in France since Qatar Sports Investments took over in 2011, winning the league nine times. They have also had success in France's domestic cup competitions, but have failed to win the Champions League.
The French champions relaunch their quest for the elusive trophy on Tuesday, taking on Dortmund in their opening game of a difficult group - which also features English side Newcastle United and seven-time winners AC Milan of Italy.
"When a club is obsessed with something, it's never a good sign. You have to have ambition but obsession doesn't work in any area of life," Luis Enrique told reporters on Monday, ahead of the game at Parc des Princes.
"You have to wait and see how the competition goes, football is a wonderful sport, any result is possible.
"You can play an incredible game and lose, play badly and win. As a club, we play all competitions to win them, that's the objective. It's very ambitious but it's necessary."
Defender and club captain Marquinhos (29) echoed his manager's sentiments, saying: "The Champions League is not an obsession, there isn't pressure.
"We're working because we're competitors, and the club is determined to win every competition, including this one. We know the path, it's a long one.
"We have to take it step by step, it's a very difficult competition to go after."
PSG, fifth in the Ligue 1 standings on eight points after five games, have had a mixed start under Luis Enrique, winning two of their five league games.
They were beaten 3-2 by Nice on Friday, but Luis Enrique said the ups and downs in the early portion of his tenure were par for the course.
"There's a lot of information to pass on, ideas and concepts that the players need to assimilate. I've found the team to be very receptive," the Spaniard said.
"The fans are incredible. Their support is magnificent, even when the results aren't up to scratch.
"I already have this experience, this process that takes time... I feel calm, there will be good football and good results, I'm sure of it. "
