The ex-City Ground supremo is said to have rejected an offer from Burnley this week.
Cooper was one of the ideal candidates for the post, as Vincent Kompany has left for Bayern Munich.
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However, The Athletic revealed that Cooper does not want to work in the Championship.
He is said to be seeking another Premier League job, as he believes he can excel at that level.
Cooper may be waiting to see how managers fare in the new season, with sackings likely to open up opportunities to manage top flight clubs.