"I think I've shown this season I have exactly the level it takes to be the number one goalkeeper," Areola said in an interview with French daily Le Parisien published on Saturday.
"If I don't remain the first choice that would mean the season I've just had will be for nothing," added the 25-year-old who is part of France's squad for the World Cup.
"What happens next in my PSG career will be sorted out after the World Cup."
After splitting time with Kevin Trapp last season, Areola played every minute of PSG's Champions League campaign this term while keeping 16 clean sheets in 33 Ligue 1 appearances.
"For the moment, I haven't been in touch with management," Areola said. "I don't know what they want to do. One thing is certain: if they give me the chance to stay at PSG, I will accept it without hesitation.
"Now, if they don't let me have the same amount of playing time, things will certainly be different."
Reports in both France and Italy this week have suggested Buffon, 40, could move to PSG this summer after he announced he will leave Juventus at the end of the season.