The city council is considering plans to build a Go Ape attraction in Roundhay Park, featuring aerial zip wires and rope walks.
A petition against the plans has been signed by 1,500 people, who have said say they are concerned it will be too noisy and cause traffic problems.
The consultation has been extended by the council until 17 January.
Ben Davies from Go Ape said the issue of parking had been considered and would be addressed.
"We are confident that we can overcome those issues and with any luck provide some additional car parking spaces for users," he said.
"We hope that we can be of benefit to the local area in that respect."
Richard Critchley, Chair of Friends of Roundhay Park, said: "We are frightened that we are commercialising and selling off the park bit by bit.
"It would destroy the woodland because trees would be felled and then the excessive noise that would be created by people, the character of the area would be destroyed."
Jan Rippin, who also lives nearby, added: "It is a free walking place, a woodland, you can see wildlife, you can see woodpeckers. With a big commercial event in one corner, I think it will destroy that part of the park.
Go Ape said the attraction would create 30 jobs for local people, there would not be any music or public address systems and it would encourage children to exercise outdoors.
Lucinda Yeadon, executive member for the environment and sustainability at Leeds City Council, said: "At the moment we are looking at new ways of bringing in income, and if we want to maintain our green spaces then we need to look at new ways of being able to do that."
She said the plan would bring in a "significant" amount of money but that the council had to decide if it was the right decision.
"I think we need to consider ways of bringing new attractions to the city, I think an attraction like Go Ape would be fantastic but we need to find an appropriate place for it to go," she said.
Go Ape is aimed at people of all ages and has 29 locations in the UK and 12 in the United States.
Plans to build a high-wire adventure course in a Leeds park are being opposed by local residents.