The loss-making department store chain, which secured approval last week from its creditors for a restructuring, is understood to be nearing a deal with Lancer Property Asset Management, which looks after the interests of the Middle Eastern royals.

Lancer already owns the freehold and wants to redevelop the block, which includes the London College of Fashion.

The two sides have been in talks for several months. Discussions are understood to have accelerated recently and could lead to an announcement this week.

BHS’s sale of its lease, which has 45 years left, would herald the closure of its flagship.

Last Wednesday the struggling retailer won the backing of 95% of its creditors for a company voluntary arrangement to slash the rents on more than half its 164 stores. It also said it was close to securing £60m from Gordon Brothers, an American firm. It intends to bolster its finances further through more property deals.

A year ago, Sir Philip Green sold BHS for £1 to a consortium led by Dominic Chappell, a former racing driver and two-time bankrupt. The Pensions Regulator is pursuing the Monaco-based billionaire for a contribution towards BHS’s £571m pension deficit, which is likely to be taken on by the state-backed Pension Protection Fund.

Chappell, 49, spent last week working in Switzerland and Canada. He is now understood to be holidaying in Barbados with his family.

BHS declined to comment.