The RFEF, which speaks for Vilda while he remains its women's team coach, did not respond to a Reuters request for comment.
During the World Cup, he said the team's success would not have been possible without RFEF backing for him.
He praised Vilda for presiding over the World Cup win, offering him a fresh, four-year contract with an annual salary of 500,000 euros.
The RFEF source said players were now being consulted as to whether the removal of Vilda would change their minds.
Del Amo has been nominated to speak to players on the pledge that the RFEF will renew the team's staff, the source said.
Persons:
Jorge Vilda, Luis Rubiales, Vilda, Rubiales, Jenni Hermoso, Rafael del Amo, Del Amo, Aislinn Laing, Andrei Khalip, Andrew Cawthorne
Organizations:
FIFA, Vilda's, Spain, World, Madrid Bureau, Thomson
Locations:
MADRID, Australia, Sydney