The 250-home project in the Holbeck area of the city is being developed by Legal & General, which bought the site next to the Leeds and Liverpool Canal from U+I last year.
It would be the latest of a string of contract wins for McAlpine, which is enjoying a swelling order book this year.
The scheme is situated on a surface car park site at Granary Wharf, an established retail, leisure and residential location, located next to the landmark Tower Works site and Candle House.
As well as residential, the three main build projects will together offer 8,640 sq. ft. of commercial and amenity space.
Walker Modular will provide all bathroom pods for the project, which is due for completion in 2020.