Work started on the £16m contract last week and is expected to last 18 months.
Plans include a five-a-side football pitch on the roof of the the 138-bed hotel.
The 16m by 12m pitch will be built with a retractable roof and be available for use by anyone wishing to play at the top of the ten-storey building including non-residents.
Neville is developing the scheme in joint venture with the Old Trafford Supporters Club using proceeds from his testimonial match last year.
Galliford Try beat off rival bids from BAM, McLaren Construction and Bowmer & Kirkland to land the contract.