The BBC reported that relations between the council and its chosen contractors on the £32m Connswater Community Greenway plan in East Belfast had reached rock bottom.
Problems first surfaced on the job last month and an agenda from a meeting between the council and the contractors states there is a lack of mutual trust.
The greenway would stretch from the Castlereagh Hills to Victoria Park and is a flood alleviation job which would create new cycle paths.
SIAC NI Ltd and Galliford Try Infrastructure won the £21m contract last November to build walkways, bridges and cycle paths for the project.
The BBC said issues such as land access and design appear to be at the heart of the dispute and one option being considered is a mutual termination of the contract.
