But Wikimedia has rejected his request, claiming the macaque that pressed the shutter on the camera owns the copyright of the image, not Mr Slater, who now faces a legal bill estimated at 10,000 ($19,900) to take the matter to court.
He said: "If the monkey took it, it owns copyright, not me; that's their basic argument. What they don't realise is that it needs a court to decide that.
"I've told them it's not public domain, they've got no right to say that it's public domain. A monkey pressed the button, but I did all the setting up."
Mr Slater obtained the image while he was in Indonesia in 2011 attempting to get the perfect picture of a crested black macaque.
One of the animals came to investigate his equipment, hijacked a camera and took hundreds of "selfies".
"He must have taken hundreds of pictures by the time I got my camera back, but not very many were in focus. He obviously hadn't worked that out yet."
After the image appeared around the world, it was added to Wikimedia Commons, a collection of more than 22 million images and videos that are free to use online.