Palace lost Wilfried Zaha earlier this summer, but did manage to keep hold of Michael Olise, who they locked down to a new contract.
Eagles boss Roy Hodgson wants additions before the window closes and the club are looking into signing Draxler.
They have contacted PSG, according to French radio station RMC, as they look at signing the German wide-man.
And crucially for Crystal Palace, Draxler is enthusiastic about the idea of moving to the Premier League with the Eagles.
He is keen to test himself in the Premier League, while being based in London also has appeal.
Draxler only has one year left on his contract at the Parc des Princes.
The winger has been linked with heading to the Premier League is past transfer windows, but could finally make the move this summer with Crystal Palace.
