His "hunch" is it was "copied shortly after it was composed".
Auctioneers Sotheby`s said copying the piece was "not conceivable", adding the lot would go on sale on 29 November.
Ludwig van Beethoven composed and wrote Allegretto in B minor on 29 November 1817 for an English visitor to Vienna, the auctioneers said.
Mr Cooper, professor of music at The University of Manchester, claims the 23-bar piece was written a day earlier on 28 November 1817.
He said inconsistencies in the auction item include one note D being copied as C, and double bars and natural signs do not resemble Beethoven`s handwriting.
Professor Cooper, who has studied Beethoven`s manuscripts for more than 40 years, said "quite a few things don`t stack up".
"I am thoroughly familiar with every detail of his handwriting, which is why I am certain this manuscript is not in Beethoven`s hand.
"My hunch is that it was copied from the original shortly after it was composed and that the copyist tried to reproduce it by carefully working to the best of his ability," he said.
Simon Maguire, head of musical manuscripts at Sotheby`s, said: "The experts that I have shown it to are world renowned.
"I don`t think it`s really conceivable that you can get that handwriting of music so fluently if at the same time you are trying to copy somebody whose handwriting is idiosyncratic [distinctive/unique]."
Mr Maguire has invited Prof Cooper to view the manuscript being sold.
Professor Cooper has said studying a copy is "as good as the original".
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