The 68-year-old came under fire in the wake of Saturday's 1-0 defeat to the African underdogs after he dropped star forward Cristiano Ronaldo from the starting XI.
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Ronaldo was also banished to the bench for the 6-1 thrashing of Switzerland in the last-16 after Santos took a dislike to his attitude when substituted during Portugal's final group games.
Santos instead fielded Benfica starlet Goncalo Ramos, who then netted a hat-trick against the Swiss to keep his place for the quarter-final.
Ronaldo was introduced in the 51st minute against Morocco but was unable to find an equaliser as Portugal were sent packing.
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Following Portugal's exit, Ronaldo reportedly opted not to fly back to Lisbon with Santos and the rest of the Portugal team, instead preferring to remain in Qatar.
It now appears that Santos will be relieved of his duties, as reported by Portuguese outlet A Bola.
Despite criticism from Portugal legend Luis Figo for benching Ronaldo, Santos has insisted he has 'no regrets' over his decision, insisting he introduced the five-time Ballon d'Or winner at the right time of the game.
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Speaking after the game Santos told reporters: "I don't think so, no regrets. I
" think this was a team which played very well against Switzerland. Cristiano Ronaldo is a great player, he came in when we thought it was necessary, so no regrets.
"If we take two persons that were the most upset, it is Cristiano Ronaldo and me. Of course, we are upset, but that is part of the job of the coach and the player."
It looks as though those words were to be Santos' last as Portugal boss - a post he has held since 2014.
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Should Santos part ways with the Selecao, he has left an indelible mark on Portuguese football.
He led Portugal to the 2016 European Championship trophy, beating hosts France 1-0 in the final in Paris.
Santos then steered his side to lift the inaugural UEFA Nations League trophy in 2019.
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