I have always been under the impression that the mosque on the Har HaBayis is on the location of the Kosdesh HaKodoshim. Is that accurate?
The Radva"z in responsum 691* confirms that without a doubt the אבן שתיה (and by extension, the inner sanctum) is located "under the dome". He also notes that figuring out the particulars of what used to be where on the Har Habayis is very tricky business and requires careful calculation.
*Bonus - This may also be the year construction on the dome was completed.
That said, there are modern researchers who think that it was either (a) the base of the Mizbeyach (Altar), or (b) outside of the Temple complex altogether - according to this view, the sanctified part of the Har Habayis (500x500 cubits, Middos 2:1) lay in the southern half of the present-day Temple Mount (and incidentally, according to this view, the Kodesh Hakodashim turns out to be pretty much directly behind the Kosel plaza).
This was discussed in Techumin sometime in the '90s, although I'll have to look up the exact reference.
Rav Moshe Sternbuch in his Shaalos U'Tshuvos writes that he is certain that the location of the mosque is not the exact location of the Kodshei HaKodoshim.