Pochettino has led PSG to this season's Ligue 1 title, but the Argentine is widely expected to leave the capital giants this summer in search of pastures new.
Zidane has been strongly linked with the role in Paris, as the 49-year-old is still available, having not taken on a new position since leaving Real Madrid for the second time in May 2021.
"You have to be careful what you say. Zidane has shown Madrid that he has qualities that were barely imaginable," the FFF chief told L'Equipe. "In the minds of the French, he may be a successor. But that's not my goal. We'll see. If Didier and I go our separate ways, he will surely be one of the options.
"Do you see me saying today: 'Is it Zidane who will replace Deschamps?' We'll see. Zidane might take on PSG. For the France team, you have to be free. But today, we are going to do everything to put Didier in the best conditions to win this World Cup.
"We want to defend our title. But the objective is at least the last four, as usual. Will Deschamps be kept if this objective is not fulfilled? We'll discuss that later. He is our employee, but he's also a friend. I have a very courteous relationship with him."
However, according to Telefoot, Zidane is not interested in becoming the new head coach of the French champions, who have sacked sporting director Leonardo.
PSG have managed to sign Kylian Mbappe to a new three-year contract in Paris, with Real Madrid missing out on the France international despite being certain to sign him on a free transfer.
However, despite the French connection at the club, Zidane is not said to be considering a switch to Les Parisiens, who again fell short in the Champions League this season.
The former midfielder managed Real Madrid during two separate spells, leading the club between January 2016 and May 2018 before returning as head coach in March 2019, spending another two years at the helm.
Zidane led Los Blancos to two La Liga titles and three Champions League crowns during a highly successful spell, and he was strongly linked with the Manchester United job last November when the club decided to sack Ole Gunnar Solskjaer as head coach.