The Enquirer revealed last month that McAlpine was favourite to win the two-horse race with Lend Lease after Mace and a Skanska/Tishman joint venture dropped out of the running.
A London property expert said: “It looks like McAlpine has been confirmed on this one – that is the word doing the rounds.”
The building has been designed by Foster and Partners and will be up to 500,000 sq ft, large enough to house modern media services, such as studios for its TV facilities.
Bloomberg’s new headquarters will be built on the site of the former Bucklersbury House, between Bank, Cannon Street and Mansion House.