Emery has come in for some criticism since the loss to Real Madrid in the Champions League, and the decline of his relationship with Meunier has been well documented.
"I'm not 18 years old, I'm 26 years old, I need to assert myself in a club," said Meunier, a Belgium international, who has been backup to Dani Alves this season.
"I need to show what I can do in my position.
"I'm waiting because a lot of things, like the coach, will change.
"I may have more playing time, I will have to use it, I have more confidence than two years ago.
"I see the future without pressure, I think I have grown up in my game but also mentally since I'm at PSG."