Vilda, 42, led La Roja to World Cup glory in Australia and New Zealand earlier this month, but has since been caught up in the controversy surrounding president Luis Rubiales.
Now, according to BBC Sport, the Spanish federation is seeking ways to terminate his contract as manager of the country's women's team, due to his support of Rubiales.
Vilda's coaching staff have already left their positions, while his entire World Cup-winning squad will refuse to play for their country while the president remains in his position. The 46 year old is refusing to quit after kissing Jenni Hermoso without her consent.
Vilda was pictured cheering Rubiales while he repeatedly stated he would not resign at the Spanish Federation's (RFEF) special general assembly on Friday. However, Vilda has since questioned Rubiales' conduct over the matter.
Regional leaders within Spanish football as well as other RFEF representatives now believe there are grounds to sack Vilda, following his high-profile backing of his fellow countryman.
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Rubiales stood behind Vilda back in September 2022, as 15 national-team players claimed the latter's management was affecting their mental well-being.
Only three of those 15 chose to rejoin the Spain group, who defeated England in Sydney in this year's Women's World Cup final.