The Whites have struggled to cope with the strain injuries have placed on their small squad this season and sit just five points above the drop zone in the Premier League, in 16th.
They are expected to try to do business in the January transfer window, but the mid-season buying opportunity has been one they are notoriously disinclined to use.
The club do hold a serious interest in 21-year-old Aaronson, who is on the books at Austrian side Red Bull Salzburg.
It is suggested though that with Red Bull Salzburg in the last 16 of the Champions League, a transfer in January is unlikely.
The American also has interest from AC Milan and RB Leipzig.
He cost Red Bull Salzburg a fee of $6.5m to sign from Philadelphia Union and add-ons mean the total fee is likely to reach $9m by the summer.
Philadelphia Union also boast a sell-on clause between worth between ten and 20 per cent, dependent upon the next transfer fee.
