Not with just a serial number. Look at the tubes and give us a list; next, the bands (AM, FM, Short wave); Knobs--volume, tone, band, radio/phono; Wood, bakelite, metal?. We might be able to narrow it down with this info.
Post a picture of it here in the "Antique Radio Discussions" forum:
http://www.antiqueradios.com/forums/
I'm sure someone can ID it.