Julen Lopetegui was sacked on the eve of the World Cup after his surprise announcement that he had signed to take over at Real Madrid, while Fernando Hierro, who stood in as coach and led Spain to the last 16 where they lost to hosts Russian Federation on penalties, said on Sunday he would not continue in his role beyond the tournament.
Hierro, 50, who replaced Julen Lopetegui as stand-in boss before Spain's doomed World Cup campaign has also turned down the option to return to his previous role of sports director.
Spain were eliminated at the last-16 stage on penalties by host nation Russian Federation.
Fernando Hierro is to leave the Royal Spanish Football Federation after ruling out a return to his former role as sporting director.
Spain only won one game at the World Cup, against Iran, and drew their other two group matches vs. Portugal and Morocco.
Martinez played down the links ahead of a quarter-final defeat of tournament favourites Brazil, with former Barcelona coach Luis Enrique also reported to be on the RFEF shortlist along with Michel and Quique Sanchez Flores.
Former Real Madrid player Luis Enrique has been named new Spain's La Roja boss.
"We didn't speak to anyone else, we only spoke to Luis Enrique", Rubiales said.
He previously coached Celta Vigo and Barca's reserves, as well as Serie A side Roma.
Enrique, 48, who won two La Liga titles and the Champions League in charge of Barca, has signed a two-year contract with no escape clause.
According a UK Sun report, the Real Madrid legend who took over the position just before the ongoing world Cup in Russian Federation, has also distanced himself from his former job as sports director.