The Whites are believed to have had two offers for the 21-year-old rejected by the Austrian outfit in January, with their second bid worth in the region of £20m.
With hopes of winning their ninth successive Austrian top-flight title and with one eye on their Champions League knockout clash with Bayern Munich, Salzburg were keen to keep hold of their key players, such as Aaronson, for the remainder of this season.
However, The Athletic reports that Salzburg are more likely to entertain approaches in the summer for the USA international, with Leeds prepared to test the waters once again with another cash offer.
Marcelo Bielsa is set to prioritise the signing of a centre-midfielder ahead of the 2022-23 campaign, after failing to recruit any of his targets in the winter window.
Aaronson has been a standout performer for Salzburg since joining from MLS outfit Philadelphia Union in January 2021, scoring 10 goals and providing 12 assists in 51 appearances across all competitions. body check tags ::