Newly elected Liberal Democrat councillor Jim Lowrie said the troubled project has effectively been killed off following recent protests to stop the £53 million development.
Speaking to the Edinburgh Evening News, councillor Lowrie said, 'I can't see at the moment how the Sighthill complex could go ahead. It does appear to be dead in the water.
'There is so much opposition from people in the area opposed to the loss of the park, while people don't want to lose the facilities that exist at Meadowbank.'
The project has been furiously opposed by campaigners hoping to keep Meadowbank Stadium, which will make way for a new housing development under Faulknerbrowns' plans, which would also see the sporting facility will be relocated to Sighthill.
The campaign has won high-profile backing from the likes of ex-Olympian Steve Cram and former Scotland International rugby player Scott Hastings.
A council spokeswoman said: 'This councillor was speaking personally, and his views in no way reflect the council's or even his own party's standpoint. It is an unfortunate situation, but nothing has changed in regards to the Sighthill Stadium.
'The council agreed in 2004 that the Meadowbank Stadium would be demolished and the Commonwealth Pool be refurbished, and this is still the case.'