The American has emerged as Leeds’ top midfield target in the ongoing window as they continue to deal with a clutch of injuries to key players across all departments.
Leeds initially tabled a £15m bid for Aaronson, which Salzburg knocked back and they have gone in again with an improved offer of £20m.
Although the Austrian outfit are yet to confirm whether they have turned down the improved offer for the 21-year-old, Leeds are likely to fail with their second bid.
Salzburg are keen on keeping hold of Aaronson for the remainder of the season with a view to having him in their squad for the Champions League knockout stage, but the player is keen on a move to Yorkshire.
However, the midfielder is not prepared to force his way out of Salzburg this month to push through a transfer to Leeds.
Aaronson is not minded to burn bridges with his current team by leaving mid-season ahead of the knockout phase of the Champions League.
Salzburg are claimed to be open to selling Aaronson next summer and it remains to be seen whether Leeds will turn to alternative targets if they cannot see a deal being struck for the midfielder with the Austrians.