According to the fan site Green Day Authority, a new single may be appearing on radio in April. The site had this to say:
We got in a handful of emails yesterday from people in various parts of the US saying their local radio stations said a new Green Day song, "Know Your Enemy" will be played on April 20th or 21st. Which suggests that it might be the first single. American Idiot was first played on the radio August 3, 2004. 7 weeks before the album came out. Having a single out in April would put it about a month from the full release, so it seems very likely. Even more likely since we’re hearing about it from different radio stations. But of course the band hasn’t confirmed this. We’re expecting some news about this stuff in the next couple weeks.