McAlpine has been carrying out pre-construction work on the tower and was expected to win the main deal to convert it into luxury flats.
But the Enquirer understands McAlpine is no longer part of the plans and a winning main contractor will be unveiled by developer Almacantar shortly.
Refurbishment plans for the 1960s Grade II listed structure include construction of 82 luxury flats, pool, spa, gymnasium and 42,000 sq ft of retails and restaurant space.
Almacantar and McAlpine declined to comment.