A £20,00 reward has been offered for any information that may lead to a successful prosecution
Formal identification is yet to take place and the PSNI has been contacted for confirmation.
At this stage police said specialist officers are currently carrying out a search of the Cappagh Reservoir as part of an ongoing investigation.
Mr Heagney, 47, was last seen at the end of December last year in the nearby Dromore area.
A murder investigation was previously launched and a a 50-year-old man who had been arrested last week has since been released on police bail.
On Wednesday, police issued an appeal and reward for information into the disappearance and murder of the Cookstown man.
The PSNI confirmed a £20,000 reward has been offered by the Crimestoppers charity for any information that may lead to a successful prosecution.
Detective Chief Inspector Rachel Wilson from the PSNI major investigation team said: “Damien is 47 years of age, around 5' 10" tall, of stocky build, and has links to the Tyrone area.
“The investigation team with support from specialist colleagues, have to date searched three residential properties in the Tyrone area. A number of items have been taken away for further examination.
“A 50-year-old man arrested on Saturday 6th August on suspicion of murder was later released on bail pending further enquiries.
“Specialist officers, police divers and dogs are also currently performing a search of a water reservoir in the Cappagh Area.
“I want to make the following appeal.
“Damien was last seen in the Dromore area, in the early hours of Friday 31st December. I want to appeal to anyone who saw Damien at any stage to contact us.
“We have recovered his vehicle, a Grey BMW FX6 6JXR which is currently being examined.
“We have also identified another vehicle of interest, a white Citroen Berlingo van, registration number LM58 UVW.”
She added: “We know that the Citroen van travelled in the Tyrone and Fermanagh areas between Friday 31st December and Friday 7th January. I would like to hear from anyone who saw this van during that time period.
“Finally, Damien’s dog Tyson, a three-year old black coloured Rottweiler cross breed, which was wearing a red coloured collar, is also missing.
“I would appeal for anyone who has any information surrounding Damien’s disappearance and murder to contact Major Investigation Team detectives on 101 quoting reference 1058 of 19/07/22.
“The charity Crimestoppers is offering a reward of up to £20,000 for information it receives that leads to the prosecution of those responsible. Crimestoppers is independent of the police.”