Vincent Council deferred selecting an option last week to engage a landscape architect and consult the local community.
Several councillors were keen to approve a 1m or 3m-wide garden with either a hedge or trees and shrubbery.
The plans would cost $31,400 for the smaller scale barrier or $47,400 for the larger barrier.
However, Mayor Alannah MacTiernan said this was the City’s last opportunity to bring the community together to consult on a final design.
Ms MacTiernan said she would not like to see council invest funds into the park only to see so many residents remain unhappy.
‘I do think that we haven’t quite got this right,’ she said.
In January, the Guardian Express reported that the proposed works had been split into three options for the public to vote on.
These included providing an off leash dog area with a permanent barrier, a semi-permanent barrier, or not to make any changes at all and for it to remain an on-leash dog area while sport was in play.
In a letter sent to residents within 500m of Forrest Park, Ms MacTiernan said the City was struggling to reach a consensus over the best way to balance competing uses for the green space.
Despite high numbers calling to scrap changes, council voted to further investigate barriers for the park in a bid to ease problems.
During last week’s debate, Cr Matt Buckels said he did not like any of the six barrier styles presented to council.
‘I can’t imagine any of these things working in this situation,’ he said.
He said a landscape architect could develop something that would provide an adequate barrier and be attractive.
Plans will go back before council in May following the workshop.