Yes, though few saw the whole picture. This was by design, and true of people living in the Third Reich as well (pre-1939 Reich and wartime Reich alike). By early 1942, people knew Jews were being sent to the East and not coming back. Accounts of concentration camps were available in the foreign press as early as 1933, though mostly from Gentiles/gadje. The Third Reich wanted to look respectable to the outside world and led tours of concentration camps to show how humane the camps were, just places to "reeducate" dissidents. See, for example, "Nazi Prison Camps to be Permanent" from the New York Times on 27 July 1933 (Page 7), and its penultimate paragraph: "Talks with the two commanders [Theodor Eicke and Michael Lippert] convinced the correspondent that both honestly and sincerely believe that their task is pedagogic rather than punitive and that both feel sincerely sorry for the misguided non-Nazis who have not yet found the true faith." The unnamed reporter shows his newsman's savvy but cannot get names or detailed input from the inmates hand-picked by Eicke for interviews conducted in front of both Eicke and other prisoners. The Times' magazine section on Valentine's Day of 1937, meanwhile, included a full-spread feature with photo illustrations titled "Life Inside a Nazi Concentration Camp".

It helped that many of the early prisoners were people Western readers of mainstream press did not find sympathetic, like communists, anarchists, petty criminals and the mentally ill. Underground newspapers in Europe took these claims much more seriously. While most famous on this subreddit (probably) for her work refuting Holocaust denial, Deborah Lipstadt also wrote a book called Beyond Belief: The American Press and the Coming of the Holocaust, 1933-1945 (1986) which may be of interest to you.

Many versions of this question have been answered before on the subreddit, since questions about "What did [Churchill/Roosevelt/Eisenhower/Stalin] know, and when did he know it?" are very popular.

/u/Estherke has previously answered:

• What was known about Treblinka from the outside?
• During WW2, what did citizens of European countries other than Germany, Poland and neutral countries knew [sic] about the Holocaust?
• How did it become common knowledge that Nazi Germany was killing its Jewish population?

These and other answers by /u/kieslowskifan and /u/commiespaceinvader are featured in:

• To what extent was Hitler able to keep the true brutality of his concentration camps secret from the Allies, and the German people?

EDIT: (I would venture to say they were more Himmler's camps than Hitler's camps, but the concentration camps were a system with thousands of employees and middle managers fighting with one another for money and prisoners. See also Hitler in Great Man Theory and When did Hitler go crazy?, written by commiespaceinvader, which also apply to Himmler, Eicke, etc.)