Last month the council called for public submissions over plans to build one at Yarra Vista Park in Jandakot, the area with the most dog owners in the City of Cockburn.
But Atwell residents unable to exercise their dogs off the lead at Harmony Primary School have made a push for a second park.
Reserves on Tranquil Gardens and Kinship Way, both in Atwell, have been identified as two potential sites.
The Kinship Way proposal is the most likely option at this stage, with a report to be put to the council after public consultation.
Resident Bill Westhoff said a dog park would be perfect for the many local people keen to exercise their dogs together.
‘I am certain it will help keep my group together, and as a result draw more people in to come and socialise their pets, and this is really an important point,’ he said.
‘It’s also good for the owners to catch up to have a chat and swap stories of the day’s events and upcoming activities.’