Alexander and Caesar Ailurophobes?

The Daily Mail excerpts some questionable things from a Pointless Things compendium, inter alia:

[…] Some famous people apparently had ailurophobia – a fear of cats: Alexander the Great, Julius Caesar, Genghis Khan, William Shakespeare, Louis XIV, Napoleon Bonaparte, Isadora Duncan, Benito Mussolini and Adolf Hitler. Oh, and Dwight D Eisenhower is said to have had his staff shoot any cats seen on the grounds of his home. […]

This seems to be a pretty standard list repeated all over the interwebs, but I’m really curious … does anyone recall a story/anecdote in an ancient source which might have given Alexander and/or Caesar the ailurophobe tag?

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