Barneys is understood to be one of the anchors of Australian developer Westfield's White City development.
The department store will anchor the site's luxury goods mini-mall, alongside Tiffany, the upmarket jeweller that is among a number of retailers believed to have signed to what will be one of the UK's largest shopping centres.
The White City development will span 1.6 million sq ft (148,640 sq m) and is set for completion by 2008.
The company has revealed four headline anchors, Marks & Spencer, Next, House of Fraser and Next, which will sit in the main shopping centre.
Barneys is a New York landmark store famous for its window displays, shopping bags, Sales and regular appearances in US sitcom Friends.
Westfield had no comment to make.