It's possible, but not easy. Who you do it depends on what type of background noise you're talking about:
If you're talking about more transient types of noises like a door closing or something like that, those are probably the easiest (though still not real easy to do well).
If you're talking about ambient room noise, computer fans or air conditioning, or that kind of thing, it's rather harder, but possible. If can re-record the problem track(s) it would be faster, but if you cant' fixes to the current tracks can be made.
If you're talking about removing bleed from other instruments, there are some tricks that can possibly be done, but it's *extremely* difficult to the point where your'e probably far better off re-recording the probelm track(s).
Let us know just what kind of noise you're referring to, and maybe we can narrow down the prognosis for you.
G.