A few years ago I took out a book from the library a biography of Magda Goebbels by Anja Klabunde. In it she writes uncategorically that Magda and Chaim were erstwhile lovers from soon after WW1 in Berlin. There is no doubt that she was friendly with the family and especially Chaim's sisters.
From here the business gets murky. Klabunde writes that Magda was definitely Chaim's girlfried and even attended Zionist meetings with Chaim in Berlin. Where Klabunde got her info, I cannot say. The official Israeli and Zionist position is that Arlosoroff was killed by a Jewish Revisionist bullet and Jabotinsky was to blame. These 2 positions are obviously incompatible so there are obvious untruths and misinformation involved.
Arlosoroff's granddaughter is a famous journalist in Israel working for the liberal Haaretz press. I wrote her a letter asking for clarification on the matter. She passed my query on to her father - Chaim's son Saul - who I think is still alive. He wrote back to me and I still have a copy of his reply. He is clearly tired of the matter especially since Menachem Begin launched a new enquiry into the matter of Chaim's death. Saul maintains to the end that the Revisionists were to blame and that Chaim and Magda were never involved. Unfortunately this does not end the matter. The History Channel maintains that when Chaim was in Berlin in 1933, he and Magda were still sexually involved altho she was already married to Joseph Goebeels and Chaim was also married to a Jewish woman back home in Palestine. Again, where this info comes from I cannot say.
Apparently Chaim was so incensed with Magda about her marriage to a top Nazi that he drew a gun on her and shot at her but missed. She was then so angry with him that she would not accept his apologies. What is also interesting is that her previous step-father Friedlander whose name she adopted was interned in a concentration camp where he died in 1938. Why did she not rescue him? It seems that she was completely Nazified in her opinion of Jews! Hell hath no fury like a woman scorned. In a subsequent trial the two Jews accused of shooting Chaim were acquitted. In answer to your question, of course Goebbels would have known about Chaim. These Nazis were very well informed especially Goebbels.
It must have been embarrassing that the most prominent Nazi woman was previously involved with a Jew! Goebbels would have told Hitler he wants Chaim dead. When you read up on the Transfer Agreement between the Zionists and the Nazis, it is clear that Hitler backed this right up to 1941 even after the killing of Jews had already begun in Poland since 1939. Hitler would have said that Chaim cannot be killed in Germany which would jeopardize the delicate negotiations. The fact that Chaim was shot a mere 2 days after he returned from Germany seems to indicate a connection between the two events. To me it is perfectly obvious that Magda, Goebbels and Hitler were to blame for Chaim's death and not the Revisionists. Yet the Zionists claim otherwise to this day.