The 19-year-old came through the youth system at PSG before making his first-team debut in November 2016.
The teenager has not been involved in the early weeks of the campaign, however, and it had been thought that he would leave the French giants before the transfer window closed for business.
Callegari has confirmed that Genoa were interested in his services, but the Italian side could not agree terms with PSG.
"It's true that I wanted to leave PSG this summer, but they couldn't agree terms with Genoa," Callegari told Le Parisien. "It'll be a learning experience for me.
"It's part of the life of a football player and it's certainly not the first time this sort of thing has happened. I had also told PSG that I wanted to leave in January, but I won't let it get me down. On the contrary, it'll make me stronger."
Callegari has earned seven caps for France's Under-19 team.