The Whites reportedly still hold an interest in the 21-year-old attacker ahead of next summer’s transfer window.
The Yorkshire giants are believed to have had two offers for the youngster rejected by Red Bull Salzburg in January, with their second bid worth somewhere in the region of £20m.
The Athletic reports that the Austrian outfit are more likely to entertain approaches for the USA international, with the Premier League outfit prepared to test the waters once again with another cash offer.
Leeds head coach Marcelo Bielsa is set to prioritise the signing of Aaronson ahead of the new campaign, after failing to recruit any of his targets in the most recent window.
Aaronson has played a starring role for Salzburg, contributing 10 goals and 12 assists in 51 appearances across all competitions.