Asiana is a Star Alliance carrier, and should have access to Star
Alliance partner award space, which you can generally search for on the websites of United or Air Canada.
It seems like most US airlines from United (especially since the co merger) to Delta website are incompetent, especially when it comes to
finding partner award space.
But call first to see if they even see
the partner award space you see.
Many of the main US carriers don't show all of
their partners award space.