Tell Ibrahim, the Biblical Cutha, for which I had sought permission to excavate, is one of the ruins suggesting the crescent and star ; the temple is the star, but the crescent is very irregular. A canal bed, some three hundred feet wide, separates them. We rode up the steep slope of the temple mound and dismounted on the summit by the little tomb of Abraham. It was because of the sanctity of this tomb that permission to excavate here was denied me. Visible from the tomb are the date palms bordering the shores of the Euphrates, and over beyond them is Ibrahim Khalil, and there stands another sacred tomb of Abraham. The tomb is by no means impressive. The building, measuring about thirty by fifteen feet, is constructed of the square, Babylonian bricks from the ruins beneath it, and surmounted by a conical dome. The doorway, leading to the antechamber, has been partly walled up. The dust on the floor had long been undisturbed, for pilgrims seldom visit the place. The inner chamber, lighted by a small opening in the dome, contains only a plaster mound to mark the grave ; on it were lying a fragment of a marble slab, a broken earthen pot, and a faded green rag torn from the turban of some pious pilgrim. Rassam claims that while excavating at Tell Ibrahim, he rebuilt the tomb ; had he been less zealous, this one of the many sacred graves of Abraham would probably have been forgotten by now.Ibrahim Kallil, the other site of a tomb of Abraham in present-day Iraq, was also mentioned in a much earlier travelogue by Claudius James Rich who visited there in 1811.
We arrived at the Birs about half-past eleven. There are vestiges of mounds all round it to a considerable extent, and the country is also traversed by canals in every direction. The soil round the Birs was sandy. To the north of it runs a canal called Hindia, dug for the use of Mesjid Ali, by order, and at the expense of, Shujah ud Doulah. Close to the Birs, or at about a hundred yards from it, and parallel to its southern front, is a high mound, almost equal in size to that of the Kasr. On the top of it are two koubbehs, or places of prayer. The one is called Ibrahim Khalil, where they show his burialplace, which is under ground, exactly in the style of Am ran Ibn Ali. The natives tell you that it was here that Abraham was thrown into the fire by Nimrod. This tomb has been lately repaired.So it appears that the Arabs and Muslims have had a number of places they venerated as the burial places of Abraham, not only the one in Hebron.
It appears likely that the main reason they only talk about the Hebron tomb nowadays is because it also happens to be a place that Jews worship.