The 26-year-old has been touted as a target for the Red Devils in recent months as Louis van Gaal looks to bolster his midfield options at Old Trafford.
United signed Real Madrid forward Angel di Maria in a British record £59.7m deal on Tuesday evening, casting doubt over a potential move for Cuadrado.
And Fiorentina owner Andrea Della Valle ruled out the Colombia international leaving the Florence-based outfit before the close of the transfer window.
“I can say with certainty Cuadrado is staying,” De Valle is quoted as saying by Football Italia.
“It’s a big present for the city. I hope it’s the strongest Viola of the Della Valle era.”
Colombia international Cuadrado scored 11 goals and made five assists in 32 Serie A appearances last season.
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