he doesn't own the Galaxy, he owns the Colorado team.
I have no idea if he'd be allowed to, but I guess it would kind of make sense since there have been rumblings (for forever, basically) about moving the Rams (or any NFL team, really) back to LA so may as well stick another team in that shiny new non-taxpayer-funded stadium.
He just bought a 60 acre plot of land near Inglewood. Rumors are its for the new stadium.