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Tom Holland 's set to star in an upcoming biopic about Fred Astaire ... but the late Hollywood legend's widow says the movie never got the green light from Fred's estate.

TMZ obtained a legal letter Fred's widow, Robyn Astaire , fired off to Amy Pascal -- one of the biopic's producers -- and Robyn makes it clear she hasn't authorized or granted permission for any portrayal of Fred in this biopic ... or any other film. Getty

In the letter, Robyn says Fred "was explicit in his Will that he did not want his life story to be depicted on screen" ... and he says she "fully respects and upholds those wishes."

Robyn says no biopic has been approved or endorsed by Fred's estate ... and she says if producers move forward with a movie that goes against Fred's wishes, they should

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