He died in Babylon and it was first supposedly decided to send the corpse to Siwah Oasis, in Egypt (Diod. 18.3.5, 28.3; Justin 13.4.6; Curt. 10.5.4), which is possibly how he wished things to be. Arrian, however, tells us that nearly two years elapsed while a colossal funeral carriage/float/barge/conveyance was constructed, at enormous expense. When it finally left, Pausanias (1.6.3) says it was headed back to Macedonia, to the burial grounds at Aegae. Along that route, we are told that Ptolemy intercepted the convoy and whisked the body away to Egypt, perhaps in pursuit of the original plan and Alexander's wishes (cf Strabo 17.1.8). This prompted Perdiccas to try an unsuccessful invasion of Ptolemy's nascent territory, which got him killed. The body was then in Memphis for a time and then eventually moved to Alexandria (maybe about 280 BCE), to a specially prepared building (the sema), within a gold sarcophagus. There it remained until at least 48 BCE, when Caesar visited it and then subsequently Cleopatra "borrowed" some of its rich decoration to fund her political goals. It was still in Alexandria in 199 CE when the emperor Septimius Severus ordered it to be sealed up, but only 15 years later we hear that objects are being messed with inside the tomb by Caracalla.

Then things get sketchy. By 400 CE, it seems that the inhabitants no longer know where the tomb is exactly. Information becomes increasingly vague from there. Leo the African (b. 1494) says he visited the tomb as a youngster, but it is unclear by that point what exactly he saw. The early antiquarian gentleman and adventurer George Sandys says he was shown a selpulchre in Alexandria but it is not at all clear that it was the same as was there in antiquity. I seriously doubt it.

So I would suggest that the trail had already gone cold by 400 CE, and certainly within a few centuries after that.