Promising centre-back Herrington, 18, left Australian club Brisbane Roar last winter for a move to Major League Soccer with Colorado Rapids, where he has quickly become a first-team regular.
Herrington has already won four caps for Australia and is part of the country's World Cup squad.
The Mirror reported earlier this month that Barcelona were monitoring Herrington's progress. The Athletic now reports that the Spanish giants have gone further, lodging an initial bid that has been rejected by Colorado Rapids.
Liverpool have also scouted the defender, according to the same reports, though Colorado Rapids are said to be in no rush to sell the 18-year-old.
Herrington is under contract until the end of the 2029 season, with an option for a further year.
The defender has scored one goal and provided one assist in 17 competitive appearances for Colorado Rapids since his move from Australia, a rapid rise that has already put him on the radar of two of European football's biggest clubs.
Herrington's emergence reflects a broader trend of MLS academies and recruitment systems producing young talent capable of attracting attention from Europe's elite at an early stage of their development, with both Barcelona and Liverpool clearly viewing the centre-back as a long-term project worth pursuing despite his limited senior experience to date.
Colorado Rapids' rejection of Barcelona's opening offer suggests the club intends to hold out for a fee that properly reflects Herrington's rising stock, particularly with his World Cup involvement this summer likely to further increase interest from clubs monitoring his situation. Any deal, whenever it materialises, would represent a significant return on a player who only left Australian football a matter of months ago.