* The prophecy of Calchas: Before the Trojan War, the seer Calchas prophesied that the Greeks would triumph, but that the journey home would be long and perilous. This prophecy likely planted the seed of hope in Agamemnon's mind that he would eventually return.
* News from Troy: Over the ten years of the Trojan War, news must have filtered back to Agamemnon about the progress of the war, victories, and the eventual fall of Troy. This news would have fueled his desire to return.
* The will of the gods: It's important to remember that in Greek mythology, the gods played a major role in human affairs. The gods could intervene and orchestrate events, including a hero's homecoming. Agamemnon's return, therefore, could have been influenced by divine intervention.
* The actions of Clytemnestra: While not exactly news, Clytemnestra's actions in Agamemnon's absence (her affair with Aegisthus and her plotting against her husband) create a dynamic that compels him to return. He doesn't necessarily *hear* about it, but his absence creates a situation where he must return to deal with the consequences.
It's important to note that there is no single, definitive account of how Agamemnon learns about his potential homecoming. Different sources (Homer's *Iliad* and *Odyssey*, Aeschylus's *Agamemnon*) offer different perspectives and details.
Ultimately, his homecoming is a product of his own ambition, the will of the gods, and the actions of others. He learns about the potential for his return through a combination of these factors, and it is this knowledge that fuels his desire to finally make it home.