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.

A large tipper truck was observed delivering the tyres under cover of darkness on Wednesday night.
A council spokesperson said the bonfire was on land owned by the Housing Executive (NIHE) in Ballybeen.
"The council has been in touch with the NIHE to raise the issue of the tyres at the site and to request the matter is investigated," they said.
"The Northern Ireland Environment Agency has also been contacted by the council regarding the nature and volume of the bonfire material."
Asked about the burning of tyres on bonfires on the Radio Ulster's Nolan programme, community worker Jim Wilson there was "a very, very small minority we are talking about where we have problems".
"You're talking about businesses making money out of it, and that comes down to the PSNI to deal with it."
Meanwhile, Belfast City Council said it had received reports that tyres had been collected at a bonfire at Avoneil in the east of the city.
"We have been engaging with the local community at this site to have the tyres removed and will continue in our efforts to manage the negative impacts of the bonfire which includes the burning of tyres," a spokesperson said.
Ulster Unionist Cllr Jim Rodgers said the inclusion of tyres in bonfires was "a worrying development".
He said that councillors had met the police and asked them to be "more pro-active" regarding bonfires.

Martyn Ashton, 41, from Margam, Neath Port Talbot, had set out to raise about £7,000 for rehabilitation equipment.
Friends suggested he set up a crowd funding page rather than sell his Colnago C59 bike worth £7,000.
He described people's generosity as humbling and touching.
Mr Ashton was a professional stunt cyclist, with his videos Road Bike Party and Road Bike Party 2 gaining more than 28 million views between them on YouTube.
But he lost the use of his legs in an accident during a live show in 2013.
He said equipment for people with disabilities could prove expensive so the money would be put to good use.
"I never, ever thought it would reach £50,000," he said. "I can now think long term. It's a remarkable thing."
Plans to build a high-wire adventure course in a Leeds park are being opposed by local residents.
[NEXT_CONCEPT]
Lisburn and Castlereagh Council is investigating the dumping of tyres at a bonfire site in Dundonald.
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A paralysed stunt cyclist has said he can start planning his own long-term care and rehabilitation after receiving £50,000 in donations since starting an appeal four days ago.