Under the former Real Madrid and Spain defender, who had little previous coaching experience, 2010 winners Spain lost on penalties to host nation Russian Federation in the last 16.
Fernando Hierro is to leave the Royal Spanish Football Federation after ruling out a return to his former role as sporting director.
Luis Enrique is favourite to take over as Spain manager.
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. Spain left the tournament after winning just one game.
A formal unveiling is likely to take place next week.
Remembering a world before the World Cup started is proving very hard now that we're in this utopia of brilliant football and weather so incredible that even in Manchester I've forgotten what rain looks like.
Luis Enrique led Barcelona to the treble in his first season in charge.
Before Enrique's last match as coach, Pique, a Barcelona mainstay, said: "He is one of the best coaches in history, we have won everything and these three years have been magnificent".
Molina, 47, a former goalkeeper with Atletico Madrid, Deportivo La Coruna and Villarreal, earned nine Spain caps as a player.