The Austrian Bundesliga leaders knocked back the Whites’ initial bid, believed to be in the region of £15m.
But Leeds have reportedly returned with a second, improved offer of £20m.
Whites head coach Marcelo Bielsa was asked about Aaronson at Thursday's pre-Newcastle United press conference - what he knew about the 21-year-old USA international and why he would be suitable for the way United play.
Bielsa said: "I prefer to speak about the player when it’s not a hypothetical possibility but when he’s actually our player."
Support the YEP and become a subscriber today. You'll enjoy unlimited access to the latest on Leeds United and Leeds Rhinos. With our sports digital subscription, you'll also see fewer ads, enjoy faster load times, and get exclusive content. Click HERE to subscribe.