One said: "We are in preliminary discussions. I expect to see agreements made in the next two to three weeks. There are a lot of balls in the air waiting to be caught."
Client NHS Estates launched the national roll-out last December and is due to select five to 12 "principal supply chain partners" for the four-year programme this autumn.
Some of the UK's largest contractors, such as Laing, Costain, Gleeson, Kier and Shepherd, are in talks over joint ventures. The final consortiums could include consultants such as Atkins and Capita.
Companies are seeking alliances they consider that individual firms will be unable to cope with the workload on their own.
One contracting source said: "We have been talking to a number of people. If you believe what they are saying, there will be up to £300m worth of work for each partner. That would mean that we would need to use 600 staff – more than half of our workforce."
The contractor said the nature of the programme could lead to surges of work at particular periods and in particular areas, and added: "It's a tricky one. The joint ventures will need to cover wide areas and have to be flexible if there is a sudden glut of work."
The scheme is an extension of pilots projects in the North-west and West Midlands. Five firms – Laing O'Rourke, Costain, Pearce, Norwest Holst and Interserve – were selected last year to work in those two regions.
NHS Estates is running training programmes jointly with consultant Knowles Management for bidders to learn more about the programme.