You might try adding snap-on ferrite beads to the power cord. If the monitor has an external switching power supply you could try replacing it; some of those a

You might try adding snap-on ferrite beads to the power cord. If the monitor has an external switching power supply you could try replacing it; some of those are noisy. Otherwise, if it's an older monitor, the noise is probably coming from the CCFL power inverter (an internal AC power supply that powers the fluorescent backlight.) New monitors usually use LED backlighting.