According to Brewer's Dictionary of Phrase and Fable, this expression is an allusion "to the fable of the dog that made his home in a manger. He would not allow the ox to come near the hay but would not eat it himself."
Wikipedia adds: "Although the story was ascribed to Aesop's Fables in the 15th century, there is no ancient source that does so."
© Haydn Thompson 2017