Aaronson has emerged as Leeds’ top target in the final third of the transfer window and the club are pushing to take him to Elland Road.
Red Bull Salzburg rejected Leeds’ first offer worth £15m for the attacking midfielder and are not interested in selling the American this month.
However, it has been claimed that the new bid is unlikely to cut the mustard in Austria and it is likely to be rejected.
Salzburg do not want to lose a key player such as Aaronson in the middle of the season and are expected to knock back the offer.
The Austrians are more likely to be receptive to an offer for the 21-year-old in the summer transfer window.
It remains to be seen whether Leeds go for other targets if the latest bid is rejected or continue to push to land Aaronson.
Leeds want to bring in a midfielder this month and are believed to have more than one target on their radar.