Can mammals and/or birds see / detect infra-red light?
Infrared is a fairly large part of the electromagnetic spectrum, so to get an answer best suited to your specific case, you should specify the wavelength of your LED. There is at least one study showing that ferrets (not sure if it's the best predator to worry about for what I assume is a suspended bird's nest) can see up to 920nm.

So to answer your question, yes, at least some can, but the further into the spectrum you go, the fewer there will be.

I am much less certain, however, that this would attract danger. Nocturnal predators in biomes inhabited by humans generally evolve to avoid rather than seek out artificial light sources.