Environmental health officers are working with the owners of Forthquarter Park to investigate the deaths.
It’s understood as many as ten dog owners fear their pets may have been poisoned.
Community group Friends of West Pilton has appealed for anyone else whose dog has fallen ill to come forward.
A spokeswoman for the National Grid, which owns the park, said: “National Grid is working with Edinburgh council environmental health officials to try to establish the cause of recent dog deaths which are being linked with Forthquarter Park.
“The park was opened in 2007 and we are not aware of any past environmental issues except an early issue with sewage contamination of a watercourse which we resolved working with Scottish Water.
“A regime of regular chemical and bacteriological testing of the water bodies within the park is currently in place.”
A city council spokeswoman said: “Our environmental health team are currently looking into the matter.”