The Brunswick centre, WC1, is under offer to Lazari Investments for more than the £110m asking price.
LaSalle Investment Management, on behalf of the Royal Mail Pension Plan, appointed JLL to sell the 290,000 sq ft Grade II listed mall in Bloomsbury, W1 in September.
Lazari Investments emerged as the winning bidder from a 10-strong field including DTZ Investors.
Brunswick tenants include Waitrose, River Island, New Look and Space NK.
JLL advised on the sale.