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The former defender had been sporting director for the Spanish FA before temporarily taking charge of La Roja for the 2018 World Cup following the dismissal of Julen Lopetegui.
Radio Marca claim the South American nation have now contacted the former Real Madrid star to take charge of their struggling side.
The former Madrid captain has one season of managerial experience having coached La Liga 123 side Real Oviedo in the 2016-17 but left after just one season following a mid-table finish.
Hierro netted 29 times for Spain in 89 international appearances whilst his playing career spanned spells with Real Valladolid, Madrid, Bolton Wanderers and Al Rayyan.
Hierro captained his nation and his most memorable goal was against Switzerland in a last 16 tie at the 1994 World Cup.
