PSG have long been linked with the Barcelona superstar who is in the final few months of his deal, with Leonardo recently confirming their interest.
Ronaldo's future, meanwhile, remains unclear after there were calls for the player to be sold after Juventus were knocked out of the UEFA Champions League this week.
When asked about Messi, Leonardo told RMC Sport,""We have nothing at all in relation to the future, except the idea of extending the players that we already have.
"There is nothing to contract or plan for anything. We are also obliged to measure what will be the financial results of this season.
"So, we're attentive, but there is nothing (with Messi)."
Leonardo also insisted there is no talks with Ronaldo or other player at this current time.
"What makes us happy is that the PSG is almost always in all the files. It's good. The transfer window is very fluid, there is movement.
"PSG is very desired, in general. All the great players are linked to PSG. This is something that must be valued.
"We are always in the position to speak with the great players, who would like to come. But we have no negotiations in progress regarding a new player."