The developer aims to flatten the 24-storey Marble Arch Tower to make way for two distinct new buildings of 17 storeys and 7 storeys.
Sir Robert McAlpine is also vying to build the project and was connected with the landmark scheme offering fee-based pre-construction services ahead of plans being submitted.
A source told the Enquirerthat Almacantar was now leaning towards awarding the job to Brookfield Multiplex.
The contract is expected to be worth £180m-£200m.
Sir Robert McAlpine is the main contractor for Almacantar’s other major central London project to convert the Centre Point office tower into flats where work is expected to start later this year.
Almacantar bought the Marble Arch Tower in the summer of 2011. Once the existing 1960s, 82m high building is demolished work will start on the 400,000 sq ft replacement mixed-use scheme.
The new lower rise plan will deliver 52 luxury flats, 123,000 sq ft of offices, an Odeon cinema and shops.
Construction of the scheme, located on the corner of Oxford Street and Edgware Road, is expected to start in 2015.