The night-time noise has been reported in a wide area of the County Tyrone town in recent weeks.
Fermanagh and Omagh District Council's attempts to trace it have so far not been successful.
Now, noise experts could be called in by the council as it struggles to find the source of the mystery hum.
Alliance Party councillor Stephen Donnelly said it was a serious problem for some residents.
He was initially contacted by people in the Tamlaght Road area of Omagh in late October, but in the weeks since reports of the mystery noise have spread to other parts of the town.
Mr Donnelly said people "usually characterise it as a persistent buzz or hum" that was distinct from more common noise such as traffic.
Many people, he said, had reported problems sleeping because of the noise pollution.
It was imperative that the council did its utmost to trace its source, he said.
"It may well be that it's seasonal or weather-related but these things often don't turn out to be simple and it may be a multitude of sources," said Mr Donnelly.
"What we need to do is establish the facts and get to the bottom of this and then take action to resolve this."
A council spokeswoman said the investigation had been challenging.
"Due to the wide area where the sound has been reported it is difficult to pinpoint the exact source(s)," she said.
"Officers are currently investigating the use of specialist equipment, or procurement of a specialist company, to assist in detecting the source of the noise."
A phenomenon known widely as"the Hum" has been reported across the globe over the past five decades, including in the UK, North America and Australia.
There is a range of theories as to where such noises come from, including farm or factory machinery, while some subscribe to conspiracy theories such as flying saucers.
People in Omagh say they are fed up with a persistent humming, which is disrupting their sleep.