The Brazilian's arrival left Meunier unsure of his long-term future at the Parisian club and led to him pondering a proposed move to Chelsea.
Meunier opted to stay in the French capital and fight for his place in Unai Emery's side and has since made seven Ligue 1 appearances this season.
The 26-year-old has now set the target of usurping Alves as PSG's first-choice right-back despite initial concerns over the former Barcelona defender's arrival.
"I was waiting for a signing at right-back but not Dani Alves," Meunier told Eleven Sports. "When he arrived I did not know what to think, I wondered if I would still play or stay on the bench.
"I could have left for Chelsea on the last day of the transfer window but I did not want to. I want to become the first choice by the end of the season."
The Italian has been handed just one Premier League start since the switch, however, as Cesar Azpilicueta and Victor Moses continue to operate in the right side of Conte's side.