Did Alexander the Great ever intended to conquer the west?

The answer is yes. Or perhaps no. Bear with me.

As ever with questions about Alexander, it is worth stressing that all our surviving literary sources postdate the man's death by over two and a half centuries. Fully teasing apart the mythic and the historical Alexander is incredibly difficult and potentially even a bit futile because so much of what we know about Alexander is filtered through layers of mythic constructions and responses to them. Now, these surviving sources by and large draw on sources that were contemporary, the so-called 'first-generation historians', but these do not directly survive. This creates problems, though, as it means that if a surviving source mentions something that no other source does, it's not always easy to tell if it's:

An inclusion of material from a primary source that the other sources simply neglected to include;
Based on later traditions in between the time of Alexander and the composition of that text; or
An invention or otherwise a major distortion by the author of the final work.

However, our sources broadly concur that Alexander was entertaining some sort of further ambitions. He was assembling at least one fleet for some purpose, and his training of a large corps of 30,000 Persians in Macedonian-style equipment and tactics implies that there was likely to be some ambition of further conquest that would perhaps not be as reliant upon increasingly mutinous Macedonian and Greek soldiers. The sources are all pretty accessible, so I'll start by quoting them:

Diodoros 18.4.2-6:

[2] For when Perdiccas found in the memoranda of the king orders for the completion of the pyre of Hephaestion,which required a great deal of money, and also for the other designs of Alexander, which were many and great and called for an unprecedented outlay, he decided that it was inexpedient to carry them out. [3] But that he might not appear to be arbitrarily detracting anything from the glory of Alexander, he laid these matters before the common assembly of the Macedonians for consideration.

[4] The following were the largest and most remarkable items of the memoranda. It was proposed to build a thousand warships, larger than triremes, in Phoenicia, Syria, Cilicia, and Cyprus for the campaign against the Carthaginians and the others who live along the coast of Libya and Iberia and the adjoining coastal region as far as Sicily;to make a road along the coast of Libya as far as the Pillars of Heracles and, as needed by so great an expedition, to construct ports and shipyards at suitable places; to erect six most costly temples, each at an expense of fifteen hundred talents; and, finally, to establish cities and to transplant populations from Asia to Europe and in the opposite direction from Europe to Asia, in order to bring the largest continents to common unity and to friendly kinship by means of intermarriages and family ties. [5] The temples mentioned above were to be built at Delos, Delphi, and Dodona, and in Macedonia a temple to Zeus at Dium, to Artemis Tauropolus at Amphipolis, and to Athena at Cyrnus.Likewise at Ilium in honour of this goddess there was to be built a temple that could never be surpassed by any other.A tomb for his father Philip was to be constructed to match the greatest of the pyramids of Egypt, buildings which some persons count among the seven greatest works of man. [6] When these memoranda had been read, the Macedonians, although they applauded the name of Alexander, nevertheless saw that the projects were extravagant and impracticable and decided to carry out none of those that have been mentioned.

Curtius 10.1.17-19:

[17] Alexander himself, having embraced infinite plans in his mind, had determined, after thoroughly subduing the entire seacoast of the Orient, to cross from Syria to Africa, being incensed against the Carthaginians, then passing through the deserts of Numidia to direct his course to Gades — for the report had spread abroad that the pillars of Hercules were there — [18] then to visit Spain, which the Greeks called Hiberia from the river Hiberus, to approach and skirt the Alps and the seacoast of Italy, from which it is only a short voyage to Epirus. [19] With this in view he ordered the governors of Mesopotamia to cut timber on Mt. Libanus, transport it to Thapsacus, a city of Syria, and lay the keels of 700 ships; all were to be septiremes, and to be taken to Babylon. The kings of the Cypriotes were ordered to furnish copper, hemp and sails.

The accounts of Diodoros and Curtius above are the two that most unequivocally state that Alexander was aiming at conquests in the western Mediterranean. Arrian, in the Anabasis of Alexander, suggests that his ambitions went in a different direction:

Arrian Anabasis 7.15.4:

[4] On the way back to Babylon he was met by representatives from Libya, who with congratulatory speeches offered him a crown in recognition of his sovereignty over Asia; Bruttian, Lucanian, and Etruscan envoys also arrived on the same mission from Italy. It is said that Carthage, too, sent a delegation at that time, and that others came from the Nubians and European Scythians - not to mention Celts and Iberians - all to ask for Alexander's friendship. It was the first time that Greeks and Macedonians had ever heard the names of these peoples or set eyes upon their unfamiliar dress and equipment.

Arrian Anabasis 7.19.4-5:

[4] [Aristoboulos] says that Alexander had commissioned the building of a new fleet in addition, for which he was felling the cypresses in Babylonia: these were the only trees in plentiful supply throughout Assyria, a country otherwise devoid of shipbuilding materials. To crew the ships and provide ancillary services large numbers of murex-divers and others who made their living from the sea arrived from Phoenicia and the rest of the coast: and Alexander was dredging a harbour at Babylon big enough to afford anchorage for a thousand warships, and building dockyards to go with it. [5] Miccalus of Clazomenae was sent to Phoenicia with a budget of five hundred talents to hire or purchase men with experience of the sea. The reason for this was that Alexander had it in mind to colonise the coast of the Persian Gulf ad the outlying islands, thinking that this area had the potential to match the prosperity of Phoenicia.

That Arrian's summary of Aristoboulos is accurate is corroborated by Strabo 16.1.11, which gives a similar account and also explicitly cites Aristoboulos.

There is one further account which suggests a slightly different direction, that being Justin's Epitome of the Philippic History of Pompeius Trogus, 13.5.7:

[7] This being reported to Alexander, he gave orders that a thousand ships of war should be raised among his allies, with which he might carry on war in the west; and he intended to make an expedition, with a powerful force, to level Athens with the ground.

So, what do we make of all this? Arguments over the veracity of Diodoros' account of Alexander's plans in Anglophone historiography go back to at least 1921, when W. W. Tarn published an article arguing against it, and resurged in 1939-40 when Tarn published a supplement to the earlier article, and C. A. Robinson responded with an argument for the reality of the plans despite the inaccuracies of Diodoros. The issue remains, it seems, unresolved – Atkinson, Truter and Truter's 2009 article on Alexander's last days rather shrewdly opts to state that the Carthaginian plan 'seems to have been promised', but the establishment of two fleets 'certainly' happened. While the historiography has obviously not ended with Tarn and Robinson, there really isn't much of a firm approach other than to shrug your shoulders and go with your own perspective on the reliability of the differing source traditions. And it is to the question of the veracity of Diodoros 18.4 that we now turn.