The 68-year-old Santos had been adamant that he would not be forced out of the job he has held for eight years despite Saturday’s 1-0 defeat to the history-making Moroccans in Qatar.
He accepted, however, that not everyone agreed with his decisions during the World Cup which included dropping Cristiano Ronaldo to the bench in the later matches.
“I’m leaving with the feeling of enormous gratitude,” he said in a video posted on the federation’s website.
“When you lead a group, you have to make some difficult decisions. It’s normal that not everyone is happy with the choices I made.”
Sports daily Record claims that Jose Mourinho is the federation’s number one target to take over ahead of qualifying for Euro 2024.
They would even reportedly entertain a deal to allow Mourinho to take charge of the national team on an interim basis to allow him to see out the season with club side Roma in Italy.
Asked by journalists late Thursday afternoon, when he arrived in southern Portugal for a training camp with Roma, Mourinho made no comment.
Portuguese coaches Rui Jorge (under-21s), Abel Ferreira (Palmeiras), Paulo Fonseca (Lille), Rui Vitoria (Egypt) and Jorge Jesus (Fenerbahce) are also among the potential candidates cited by local media.
Appointed coach of Portugal in September 2014, Santos won the country’s first major title at Euro 2016 and followed it up with the 2019 Nations League.
However, his time in charge also saw last 16 exits at the 2018 World Cup and Euro 2020.