Alexander wanted to do so, in effect. After conquering Persia, he led his army into western India, proclaiming his wish to continue conquering to the great encircling ocean. However, his troops - seeing the Himalaya Mountains on the horizon which made it clear that the encircling ocean was nowhere near - revolted. Against his will, Alexander was forced to turn back west. Upon his return to Babylon, though he soon started planning a campaign to Arabia, I'm not aware of any thoughts of returning east.

So, Alexander did effectively want to conquer China, or at least continue fighting his way to the Pacific Ocean. However, extending his life probably wouldn't bring him anywhere near there.