It was discovered in a bin at Vere Foster Walk on Wednesday.
It is understood that the item is not linked to the police investigation into a shooting at a petrol station on the Crumlin Road in north Belfast on Sunday in which a police officer was wounded.
The suspected firearm has been taken away for examination.

The character with a huge papier mache head was the alter-ego of musician and comedian Chris Sievey, who died in 2010.
Fans raised Â£60,000 for the tribute which was made in a Czech foundry.
Hundreds of people attended an unveiling ceremony earlier, many in fancy dress for the occasion.
Neil Taylor, who helped raise the donations for the statue, said its installation would mean that "Frank will gaze on the Timperley sunset forever".
He said: "You either got the humour or you didn't get the humour.
"Frank Sidebottom created a whole world, he was just magical. He just made a very modest living entertaining people and that's what he's enjoying doing."
Sievey set his character's life in the village, where he lived himself, and, as Frank, hosted tours of the area for fans.
He often referenced Timperley in his TV and music work, notably on his 1987 release, The Timperley EP, which featured a version of The Kinks' 1967 song Waterloo Sunset with altered lyrics that referred extensively to the village.
He also covered Sex Pistols' Anarchy in the UK, changing its title to Anarchy in Timperley.
Although best known for Frank Sidebottom, Sievey also had success in the late 1970s with his punk band The Freshies, who had a hit with I'm In Love With The Girl On The Manchester Virgin Megastore Checkout Desk.
His TV fame peaked in the early 1990s with his own series Frank Sidebottom's Fantastic Shed Show.
Next year Michael Fassbender will play Frank Sidebottom in Frank, a movie inspired by the character.

The building in Hammersmith's Margravine Cemetery, London created in 1869, has been given Grade II listing.
Families unable to immediately pay for a burial previously used to keep dead relatives in their homes, contributing to cholera outbreaks in the city.
Historic England said the store was "ghoulish and absolutely fascinating".
Director of listing Roger Bowdler said many had to keep their relatives' bodies in their small cramped homes during the early 1800s, "so you've got the living cheek-by-jowl with the dead".
The small octagonal building used for holding the dead before funerals, was an example of the facilities proposed by Edwin Chadwick, secretary to the Poor Law Commission, who led a review of sanitary conditions.
The store also addressed people's fears that their relatives would be buried before they had actually died.
The use of reception houses was phased out with the introduction of undertakers in the 1880s and the building is the sole survivor of its kind in the capital, according to Historic England.
Heritage minister Tracey Crouch said the building was "an important part of London's history" as it "gives us a glimpse into how cholera outbreaks changed Victorian attitudes to burials and public health."
Receiving the listing could help secure funding for any conservation work on the reception house.

The constitutional court will now decide whether he has violated the constitution and can be dismissed.
The BBC's Martin Vogl in the capital, Antananarivo, says the late night vote came as a surprise to many.
Mr Rajaonarimampianina has been in office for 16 months and it was hoped his election would end years of political unrest on the island nation.
Madagascar suffered five years of political turmoil beginning in 2009 when Andry Rajoelina ousted Marc Ravalomanana from power.
The coup left the country isolated in the international community and deprived of foreign aid.
Ahead of the parliamentary vote, the US embassy in Antananarivo urged the MPs to put the stability of the country first.
A suspected firearm has been found by police during a search in west Belfast.
[NEXT_CONCEPT]
A life-size bronze statue of comedy character Frank Sidebottom has been unveiled in his hometown of Timperley in Greater Manchester.
[NEXT_CONCEPT]
A cemetery's unique Victorian reception house which stored coffins to stop poor people keeping bodies in their homes, has been given protected status.
[NEXT_CONCEPT]
Parliamentarians in Madagascar have voted to impeach President Hery Rajaonarimampianina.