Portugal were one of the favourites to win the competition in Qatar but were knocked out by Morocco in the quarter-finals.
The manager had enjoyed success with the national side as he helped them to the trophy at Euro 2016, just two years after he was appointed.
Portugal also won the 2019 Nations League finals under Santos.
It has been reported that former Chelsea and Manchester United manager Jose Mourinho is the Portugal chiefs’ favourite to take the job.
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