The firm is up against a strong field of bidders understood to include Galliford Try, Chorus and Kier to take the high profile fit-out and rebuild job.
A supplier told The Enquirer: “Nothing’s been officially signed off but Skanska is starting to look like it has this one in the bag.
“It’s such a big job that the client has gone for a traditional contractor rather than a fit out specialist for this one.”
The winning contractor is due to be named next month to overhaul the building, which has been dubbed as one of the ugliest buildings on the Thames.
During the £100m overhaul, 13 floors of current office space will be converted to provide a 360-bedroom hotel.
Developer Archlane also has permission to create a new roof extension from the 12th floor to provide a new bar for the hotel’s use.
The redevelopment includes extensive work to overhaul the facade of the building, which will retain its characteristic golden globes and signage.
Plans also include construction of a nine-storey extension to the rear of Sea Containers House to provide retail at ground floor level and offices above.
The Thames-side building was originally conceived as a luxury hotel but was reconfigured as offices before it opened in 1978. It is named after its original owner, an international shipping company.