I've heard that the Magi may have been influenced by the writings/teachings/prophecies of Daniel.
I think a good case can be made for this.
Some people have suggested that it was Daniel who was given the revelation that Christ would be born under a star and that's how the Magi knew about it.
An interesting case can be made for this too. It's curious that around 135 AD Rabbi Akkiba thought Bar Kokhba was the Jewish messiah. Bar Kokhba means "son of the star" and was probably connected to this:
Gen
49:8 Judah, your brothers will praise you.
Your hand will be on the neck of your enemies,
your father’s sons will bow down before you.
49:9 You are a lion’s cub, Judah,
from the prey, my son, you have gone up.
He crouches and lies down like a lion;
like a lioness – who will rouse him?
49:10 The scepter will not depart from Judah,
nor the ruler’s staff from between his feet,
until he comes to whom it belongs;
the nations will obey him.
49:11 Binding his foal to the vine,
and his colt to the choicest vine,
he will wash his garments in wine,
his robes in the blood of grapes.
49:12 His eyes will be dark from wine,
and his teeth white from milk.
Numbers
24:15 Then he uttered this oracle:
“The oracle of Balaam son of Beor;
the oracle of the man whose eyes are open;
24:16 the oracle of the one who hears the words of God,
and who knows the knowledge of the Most High,
who sees a vision from the Almighty,
although falling flat on the ground with eyes open:
24:17 ‘I see him, but not now;
I behold him, but not close at hand.
A star will march forth out of Jacob,
and a scepter will rise out of Israel.
He will crush the skulls of Moab,
and the heads of all the sons of Sheth.
24:18 Edom will be a possession,
Seir, his enemies, will also be a possession;
but Israel will act valiantly.
24:19 A ruler will be established from Jacob;
he will destroy the remains of the city.’”
