The 24-year-old, who signed a five-year deal in August, has repeatedly denied speculation he wants to leave PSG, and the Italy international did so again ahead of Wednesday's return leg against Barcelona in the Champions League last 16.
"I want to stay," Verratti told Stade 2, with PSG leading Barca 4-0 following the first leg in Paris.
"I am part of a project and there are not many like this one in Europe.
"My dream is to win the Champions League here with PSG."
Verratti continued: "I must thank the coach because he always made me confident enough to play — that was the only way I was going to get back into the swing of things.
"Now I feel good and I can play three matches in a week without physical problems or fatigue. In modern football, the most important thing is to be physically fit."