The FA said on Thursday that Mourinho had been asked for his "observations" on comments he made on Dec. 8 in interviews ahead of Sunday's game, which United lost 2-1.
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It did not, however, specify the comments under investigation or what — if any — rules might have been broken.
During a pre-match news conference, Mourinho questioned City players' ability to stay on their feet, saying: "A little bit of wind and they fall."
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He also doubted he would be allowed to make the sort of political statement that his opposite number, Pep Guardiola, had when wearing a yellow ribbon in apparent protest against the imprisonment of pro-independence politicians in Catalonia.
The FA is already investigating an incident after the match in which milk was thrown at Mourinho after he reportedly complained about City's "excessive" dressing-room celebrations following their victory at Old Trafford.
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