I know a horse and a donkey produce a mule and mules can not reproduce. Can a human and a monkey make...?

Question

a sterile off spring?

Answer 1

No.  Humans are not cross-fertile with any other species.

Answer 2

Some people think that Neanderthals were a different species from us humans but could reproduce with us to make sterile offspring. This is not confirmed, though.

Since the Neanderthals died out about 40,000 years ago, there have not been any primates closely enough related to us to allow this to happen.

Answer 3

Recent DNA studies show that humans diverged from chimpanzees about 6 million years ago.  There is further evidence of cross breeding about 4 million years ago.  But as near as anyone can tell, humans can't cross breed today.

There is an "ewe, gross" factor.  But remember that 4 million years ago, our ancestors were not modern humans.  And if the chimpanzee DNA codes are still present in humans, they have a good chance of being important still.