Yes, there are several cases of people outside the project figuring out it was occurring. The most famous is that of Georgii Flerov, a Soviet scientist who realized that the sudden apparent lack of interest in fission research in the United States had to be the result of heavy official secrecy and an all-out effort. My favorite example (which to my knowledge has not been published anywhere yet) is of a delegation of scientists from India who came to the United States in early 1945 and asked to be taken to see where the uranium was being enriched. They claimed (during their subsequent interrogation) that it was obvious that the US was working on such matters.

There were also several leaks during the war (my favorite is this one) which came awfully close to the truth. That something of this sort was being done under the code-name of "Manhattan" was something of an "open secret" in Washington circles towards the end, though of course it is one thing to have rumors and speculation and quite another to know something to be really true.

It was a large project, employing about 1% of the US civilian labor force during the war, at several gigantic-but-secret sites, with an unusual amount of official secrecy, researching a topic (nuclear fission) that was itself fairly well-known in scientific circles and had been published about on the front page of the The New York Times. That there were a few people who figured it out based on speculation and little hints is not surprising; that most people, including the German and Japanese intelligence organs, appear to have been totally ignorant of the scale of the work is the more interesting thing, really.