Two of the animals suffered internal bleeding following visits to Forthquarter Park in Granton.
Environmental health officers are in talks with the dead dogs' owners.
However, there are no plans to carry out tests at the park, which is owned by the National Grid and sits beside a former gasworks.
Extensive ground decontamination work was carried out before the park opened 10 years ago.
John Young, whose dog Holly had to be put down, said: "I was in the park with her last Sunday and we did our usual walk and went home.
"As I was getting into the house she slumped on the floor. I thought it was strange but helped her up and she slumped again.
"I kept an eye on her that day and she wasn't getting better so first thing on the Monday I took her to the vet.
"She was kept in overnight and put to sleep the following morning.
"It was awful, the vet told me she had severe internal bleeding so I told him to put her to sleep."
A spokeswoman for the National Grid said they were in contact with the City of Edinburgh Council's environmental health team, and their advice was that there was no need to close the park.
The owners of an Edinburgh park which was visited by six dogs who later had to be put down have been told there is no reason to close the area.