The England left-back is United's longest-serving player, but was not included by Amorim in his leadership group for the new campaign.
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The Sun says the decision has left Shaw hurt and angry, with the defender already exploring the prospect of moving to the Saudi Pro League this summer.
United skipper Bruno Fernandes heads a leadership group, including Harry Maguire, Noussair Mazraoui, Lisandro Martinez, Diogo Dalot and even back-up keeper Tom Heaton.
Shaw's disappointment has been noticed in training, the fullback has less than two years to run on his contract.