A common quotation attributed to Alexander the Great is as follows.
Bury my body, don't build any monument. Keep my hand outside so that the world knows, one who won the world had nothing in hand when he died.
Did he said it? Is it documented reliable-where?
It is doubtful, we have not a direct record of his own words and it did not happen anyway.
We have today only secondary sources about Alexander the Great
We know that primary sources existed (Aristobulus, Callisthenes, Ptolemy) and were used by the secondary sources we have (Arrian, Plutarchus, Curtius). One of his main biographers, Aristobulus, who used to be a close friend, an architect, a man of letters and officer in the Macedonian army, was keen to present Alexander as a benevolent and socializing philosopher-king instead of only a very successful, abusive and violent conqueror. He adds his own interpretation and explanations of Alexander's behavior. One of the main other source, Callisthenes was not very critic either. Ptolemy was establishing his legitimacy as the new ruler of Egypt.
Another attributed quotation exists on the subject of burial and glory
A tomb now suffices him for whom the whole world was not sufficient.
It is at the same time sufficiently different and sufficiently close to suggest fabrication from common elements.
However, one could easily assign the OP's quotation to visits of Alexander to famous tombs of conquerors and mythical heroes
Arrian among others reports that Alexander visited Protesilaus' tomb (An. Alex. 1.11) then Achilles' tomb (1.12) and complained there about the lack of a great writer or poet to celebrate his deeds. Alexander visited Sardanapalus' tomb in Anchialus (An. Alex. 2.5), ordered the tomb of Cyrus restored (An. Alex. 6b.29) and questioned the gardians of this tomb to find the authors of the profanation.
This and many aspects of his behavior is not compatible with a simple burial
Note that the religious tradition of the Macedonians would have him buried in the homeland, in Aegae, with great ceremony, with previous kings and that Perdiccas, one time his successor, had organized the corpse to be sent there during 322 BC from Mesopotamia after having been placed in a gold decorated sarcophage.
His corpse was an object of political, religious and military conflict immediately after his death. Ptolemy succeeded in having it transported to Egypt, in Memphis then in Alexandria, where a monument was constructed. So we cannot really know what he wanted as all of his close companions (Antipater, Seleucos, Nearchus, Ptolemy, ...) had diverging interests about this subject.
Sources:
Arrian's Anabasis translated in english in an affordable edition but I have used my own copies of the Loeb Library Edition.
An excellent biography of Arrian
Pothos A site dedicated to Alexander
Alexander The Great related articles on Livius by Jona Lendering
Mary Renault's novel doesn't portray him as having said that, nor anything like it.
The fact that she doesn't mention it is significant: I think that she includes every known/accepted fact/story about his life (and, for the sake of the novel, adds details where the details aren't known: so the fact that a detail is in the novel wouldn't be significant necessarily, but the fact that something isn't in the novel is significant).
The novel does add that a) succession wasn't assured (e.g. no primogeniture, no automatic transmission of the throne to his child); b) burying the previous king was a ceremony performed by the next/newly-chosen king (which explains why his body was an object of political/military value).
