"The confirmation PCR tests carried out on Wednesday 9 June were negative. The counter-analysis has confirmed the result in the last few hours... suggesting (Tuesday's result) was a false positive," the RFEF said.
The announcement came as Spain prepared to vaccinate its entire Euro 2020 squad just days before the start of the tournament.
The sudden decision was taken after Llorente's diagnosis on Tuesday, two days after captain Sergio Busquets tested positive.
Since Sunday, Spain's entire Euro squad has been in isolation, with the team's management on Tuesday saying it had set up a "parallel" squad of 17 reserves who may have to play if infections spread among its players.
"We are going to vaccinate all the players in the Spanish squad" with the (two-dose) Pfizer vaccine administered by the Spanish military, Health Minister Carolina Darias said on Wednesday evening.
Spain are due to open their Euro campaign on Monday, playing Sweden in Group E in the southern city of Seville.