[nuccy]

Noise cancelling works by shifting the sound waves of noise, which come into your ears. The ups and downs (of pressure) in the sound wave are added together, cancelling the wave altogether. Each ear get different noise, so the microphones should be as close as possible to each ear and work absolutely independently. Thats why microphone of your laptop is not of any help here, it simply gets completely different noise, which cannot cancel out one getting into your ears. This is more physics than software.

[dmurray]

With two different microphones on the laptop, you could triangulate sources of noise and figure out what will reach your ears. With three or more, even better. This sounds like a difficult and interesting signal processing problem, but I wouldn't rule it out.

[StavrosK]

It would also have to know where each of your ears is in relation to the microphone with millimeter accuracy.