The Burman Bush Nature Reserve, in Morningside, could be closed temporarily following the murder of local musician, Simon Miliken.
It's understood the 60-year-old and a friend were accosted while out walking on Friday afternoon.
His friend managed to escape but Miliken was found stabbed to death, the following morning.
Ward councillor, Martin Meyer says for the last month, he's been working with the community to try and improve security at Burman Bush.
"We've started setting up a conservancy to help improve the situation in the park - to get people to use the park in a safe environment. We've also managed to find some fencing to fix the fence. Many people come into the park using the holes in fence. Unfortunately, all these measures are too late for Simon who tragically lost his life," Meyer said.
Meyer says it's a wonderful place for the community and they don't want it permanently closed.
"I will be asking that the Parks Department temporarily closes Burman Bush until we can improve the situation - to secure the fence, and improve security. We as a community can take back Burman Bush," Meyer said.