Charity OnSide, which already runs eight youth zones across England, has submitted a planning application for the project to Barnet Council.
The local authority will contribute £4.2m towards the development costs of the state-of-the-art youth facility, which will be open to all young people seven days a week.
OnSide has committed to raising the remaining capital costs as well as annual revenue expenses of £1m, which it will source from charitable trusts, grants and private donors.
Named Unitas, the centre will provide 20 activities a night including football, boxing, climbing, creative arts, music, drama and employability training, for a 50p entrance fee.
Barnet Youth Zone chair Keith Black said the site would provide a "spectacular addition to Barnet's current youth provision" if the council granted planning permission.
"This is an important milestone for Unitas and an extremely exciting one for the young people of Barnet," he said.
"A lot of hard work has gone into getting developments to this stage but this is just the start."
OnSide hopes to open the youth zone in 2018. It is the fourth project the charity is working on in London, with others in Croydon, Barking and Dagenham and Hammersmith and Fulham local authority areas currently in the pipeline.
The youth charity has ambitions to create 100 youth zones "within the next generation".
