Jose Mourinho is being seen as a leading candidate to take over as Portugal manager after Fernando Santos quit following the team's World Cup quarter-final loss to Morocco.
The Portuguese football federation (FPF) said in a statement that an agreement was reached with the 68-year-old Santos "to end the journey of great success that began in September 2014".
"I'm leaving with the feeling of enormous gratitude," Santos 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."
Santos, who has been widely criticised for his tactics, became Portugal coach in 2014 and led the country in 109 matches. They won the European Championship in 2016 and Uefa's inaugural Nations League in 2018-19.
The FPF added that it "will now launch the process to choose the next national coach".
Sports newspaper Record claimed that Mourinho is the federation's top target to take over ahead of qualifying for Euro 2024, which gets under way in March.
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, according to AFP citing local media.
Mourinho, 59, has yet to coach at international level but has an impressive record at some of Europe's heavyweight clubs. He has managed Porto, Chelsea twice, Inter Milan, Real Madrid and Manchester United.
Mourinho won three Premier League titles with Chelsea, two Serie A crowns at Inter and a Liga win at Real.
He also coached Porto to 2004 Champions League victory and repeated the feat with Inter Milan in 2010.
In May this year, he led Roma to the Europa Conference League title, the club's first ever major European trophy.
