Hi there,
I am not a pro in constellation, but the Sun is not part of or into a constellation.
You have to understand where the idea of constellation comes. When our ancesters were looking at the sky (at night) they thought that it was a roof with stars hanging from it. They also noticed that these stars were "motionless" from one another. Therefore, they thought of arranging and defining the sky from the different shapes the stars were forming. Enough of this history bull crap.
The Sun being part of (and the center) our solar system, it's relative position in the skye will keep on changing compared to the stars. Therefore, the sun will eventually cross the constellation from the ecliptic (for which there are twelve), but that's it.
Cheers