The 23-year-old has made 12 Premier League appearances for the Blues - all of them as a substitute - since his £33m move from Marseille last summer and has only played the full 90 minutes in the FA Cup and the EFL Cup.
According to L'Equipe, Les Parisiens are in the market for a strike partner for Edinson Cavani after Hatem Ben Arfa failed to fill the void left by Zlatan Ibrahimovic's departure for Manchester United.
The publication reports that Batshuayi's eligibility to play in the Champions League is a key factor behind a potential deal, with Unai Emery's side due to come up against Spanish giants Barcelona in the last-16 stage.
The defending champions also face a tough challenge in the league this season, sitting third in the table and trailing leaders Nice by five points at the halfway point.
Batshuayi, who still has four-and-a-half years remaining on his contract at Stamford Bridge, is likely to cost at least the amount the Blues paid for him just six months ago.