But the 53-time German international has not been receptive to the idea because he is settled in Paris.
PSG sporting director Leonardo wants to offload several players before adding new faces to the squad.
Draxler, who started seven games in Ligue 1 last season, is one of the big earners Leonardo wants to shift.
The World Cup winner has one year left on his PSG deal, but is in no hurry to leave the French capital and Leeds have an uphill task of convincing him.
PSG paid €42m for Draxler in January 2017, but he is no longer a regular in Thomas Tuchel’s side.