The Sun says the Gunners have been told to cough up £40 million if they want Draxler.
The Gunners have made another move for Paris St Germain's forward and contacted the French club over his availability.
Draxler, 24, is seen as the ideal replacement for Alexis Sanchez if he were to move next month.
Arsenal will go to £30m for a player they have tried to sign in the past — but have indicated that they will only buy if they sell Sanchez.
Arsene Wenger is willing to sell the player — who is out of contract in the summer — but only if he can secure a suitable replacement first.