Here is a source that has some discussion along with the supposed Arabic original, although curiously it does not provide a full translation. The key phrase is something like "...we have so far killed about three million of them." You can translate it with the Google app on your phone.
http://www.trafoberlin.de/pdf-Neu/Amin% ... ocaust.pdf
A few points I would make.
-The passage is some memoir rather than a diary entry
-Al-Husseini died in 1974
-This was not published until 1999
The proof of something like the Holocaust cannot hinge on a statement like this from decades after the war that we can't even confirm. If the statement is genuine and hasn't been tampered with, it is also quite possible he was influenced by postwar Holocaust narratives.
Another point here is that Jews, specifically Zionists, have long had something of an obsession with the Mufti and have long sought to enhance his role in the "Holocaust" (for rather obvious reasons). Peter Novick talks about the curious overemphasis on the Mufti in his book Holocaust in American Life.
There are records of Himmler meeting and discussing Jewish policy with Mussolini around the same time (Nov 1943). Himmler made notes on this in 1943. Some authors like Walter Laqueur have claimed that Himmler told Mussolini about the "Final Solution" (in the exterminationist sense) but in fact he did not describe any extermination program but rather something closer to the revisionist version. The other side will either lie about the Mussolini meeting (Laqueur) or claim that Himmler lied to Mussolini and soft-pedaled the actual policy. The revisionist position would be that Himmler gave him a roughly accurate account of the policy. My guess would be that Himmler would have told Al-Husseini something similar to what he'd told Mussolini.