Assalaamu alaykum. Is it true that each heaven is like a ring in the desert compared to the one above, as Al-Aloosi stated?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallahu ‘alayhi wa sallam, is His slave and Messenger. 

Al-Aloosi said, “The reported text reads, 'The size of the earth compared to the first heaven is like the size of a ring in a desert; the size of the first heaven compared to the second is like the size of a ring in a desert, and so on, until the seventh heaven. The size of the seventh heaven compared to the Kursi of Allah is like a ring in a desert, and the size of the Kursi compared to the Throne is likewise.'” [Rooh Al-Ma‘aani]

However, Al-Aloosi did not mention the chain of narration of this report, nor the source from where he quoted it. We could not find any reports to this effect in the books where such a report might be found. Al-Biqaa‘i mentioned this topic in his book Nathm Ad-Durar fi Tanaasub Al-Aayaat was-Suwar but did not state that it is a hadeeth. He said:

“In the verse {...created seven heavens in layers} [Quran 67:3 and 71:15], the heavens are described as congruent layers, one layer above the other, in an indication that they are symmetric. This is only possible if the earth is spherical and the first heaven surrounds the earth the way the eggshell surrounds the egg from all sides, and the second heaven surrounds the first in the same way, and so on, until the Throne of Allah surrounds all. The Kursi, which is the closest of them to the Throne, is like a ring thrown in a desert in relation to the Throne. So, what do you think (the likeness of) what is below the Kursi would be? Each heaven, to the one above it, is of the same proportion. This is established by astronomers, and there is no evidence in the Sharia contradicting it; rather, the apparent indications of the texts conform with it.”

Allah knows best.