The Enquirer understands the firm had been up against Bouygues and Galliford Try in the bidding to deliver the £60m Hale Wharf project, which will involve two high-rise buildings of nearly 250 homes.
A source said: “It is now looking like McLaren will secure the project.”
The scheme, which is being developed by Muse and the Canal and River Trust next to the River Lee, is expected to start in the summer and will involve build a pedestrian bridge for access from nearby Ferry Lane.
Designed by Allies and Morrison, the two brick-built blocks in phase one, will rise to 21-storeys and 16-storeys.
Consultant Ramboll is the civil and structural engineer with Hilson Moran acting as services engineer on the scheme.
In total up to 505 new homes (35% of which will be affordable tenures) will be created at Hale Wharf, over two further phases of canal-side housing rising to around five-storeys. The total projects is worth around £130m.