Construction information specialist Glenigan said Kier, McAleer & Rushe and H & J Martin are on the shortlist for the job.
The Enquirer understands that Willmott Dixon was also in the frame but has stepped away from the scheme.
Nobu Hospitality confirmed this week that work can now start on the Willow Street site which is due to open in early 2016.
Preparation work is now underway at the site which will be home to a 156-room hotel.
Food and drink at the hotel will be overseen by chef Nobu Matsuhisa.
The scheme has been designed by Ben Adams Architects and Studio PCH. Additionally, the hotel will feature banqueting and meeting rooms, a state-of-the-art fitness center and modern amenities combined with superior service.
Trevor Horwell, chief executive officer of Nobu Hospitality, said: “The Nobu Hotel Shoreditch in London is our first European hotel joining our growing portfolio collection of hotels covering select locations in the Americas, Middle East and Asia.”
The hotel’s five stories will be fractured into angular, fair-faced concrete balconies which combined with cantilevered corten steel beams, form a seemingly frayed edge to the northern facade.