He revealed that great players like the Argentine will always be of interest to the French club.
Messi will be a free agent at the end of this season and it will be interesting to see if PSG can convince him to join them.
The player has been linked with a move to the Premier League as well with Manchester City.
Leonardo said: “Great players like Messi will always be on PSG’s list. But this is of course not the time to talk about it, or to dream about it.”
Meanwhile, Leonardo has also given an update on the futures of Kylian Mbappe and Neymar.
The PSG director hopes that the two players will continue at the French club beyond this season but they will have to make their own decision and the club will not beg them to stay.
“I hope they are convinced that PSG is a good place at the moment for a very high level and ambitious footballer,” added Leonardo.
“We just have to find an agreement between their desires, their requirements, our expectations and our means.
“We don’t have to beg them: ‘Please stay’. It’s discussed more than that. Those who really want to stay will stay. We talk regularly and I have good feelings on these two issues.”
Mbappe has been linked with a move to Real Madrid recently and Neymar has been linked with a return to Barcelona.
It will be interesting to see if the French outfit can agree on new contracts with their star attackers.
If they manage to keep both Mbappe and Neymar at the club and then sign Lionel Messi on a free transfer, they would have the best attack in world football.
PSG will be hoping to win the Champions League soon and having an attacking trio of Messi, Neymar and Mbappe would give them a great chance of achieving their goals.