Neville has been granted planning permission to put a five-a-side football pitch on top of the the 138-bed hotel.
He is developing the £20m scheme in joint venture with the Old Trafford Supporters Club using proceeds from his testimonial match last year.
Construction information specialist Glenigan said BAM, McLaren Construction, Galliford Try and Bowmer & Kirkland are bidding for the job.
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.
Building work is expected to start in January 2013 with the hotel open for the 2014-15 season.