We can assume that he knew a lot.
First of all, the Nazi persecution of Communists was well publicized by the Nazis. The new hard line against the communist, including their imprisonment in Concentration Camps or prisons (see Ernst Thälmann) as well as the murder of several prominent figures was a propaganda success for the Nazis. One of their major political agendas had been the defeat of the communist threat even prior to their election in 1933 and when the chance finally came it was practically a celebrated event.
Take the Reichstagsfire trial for example. Internationally prominent communists such as Dimitrov were accused there but managed to be exonerated and then moved to the Soviet Union where they spent the war.
Secondly, there were many emigres who fled Germany to the Soviet Union. Some of whom had manged to escape the Nazi camps and prisons, others who had been released and then fled to the Soviet Union. Of the 300.000 members of the KPD in 1932 about half had been imprisoned at some point by the Nazis and several hundred of those had fled to the Soviet Union. Among them the later GDR leader Ulbricht.
In fact, Stalin and his apparatus were especially aware of what they had been through because German emigres in the Soviet Union were kept under constant surveillance and supervision and during the mid-30s purges were one of the main targets of Stalinist terror. At least 178 of the former leadership of the KPD were killed by Stalin in 1935 to 38 after being tortured.
From all this we can assume that Stalin was acutely aware of what was going on in Germany around the same time.
Sources:
Reinhard Müller: Menschenfalle Moskau: Exil und Stalinistische Verfolgung, Hamburg 2001.
Hermann Weber und Andreas Herbst: Deutsche Kommunisten. Ein biographisches Handbuch.
Hans Schafranek: Zwischen NKWD und Gestapo. Die Auslieferung deutscher und österreichischer Antifaschisten aus der Sowjetunion an Nazideutschland 1937–1941. Verlag ISP, Frankfurt 1990.