The Spires shopping centre has been put on the market for more than £35million.
Banking firm UBS, which owns the landmark High Barnet building, says it has already received interest from buyers and will finish taking bids for the site next week.
The sale includes the High Street shopping centre and multi-storey car park, as well as the St Albans Road site of Barnet Market, which UBS took over in 2011.
A UBS spokesman said the shopping centre had been on the market for about six weeks and that the firm is seeking offers of more than £35.5million.
In October, UBS announced major renovation plans for Barnet Market, which were backed by the Friends support group and Chipping Barnet MP Theresa Villiers.
Proposals included resurfacing the site in Tarmac and installing proper drainage, replacing the hoardings with post and rail fencing and planting trees around the perimeter.
It is not yet clear if the sale of the site will affect the upgrade but planning applications for the amendments had already been submitted to Barnet Council.
Spires centre manager Graham Trotman told the Times Series he has been showing buyers around over the past few weeks.
He said: “We’ve had them coming in every other day to have a look around. It is not a worry for the centre staff as we tend to be here in situ and new owners don’t tend to come in and turf out the staff who have decades of knowledge of the site.”
The Spires currently has four vacant shops following the closure of Clinton Cards, WH Smith, an o2 shop and a gym in recent years.