If the deal goes ahead after the completion of due diligence, it will turn Morgan Sindall into the biggest social housing operation in the UK.
Carillion Housing will be incorporated into Lovell Partnerships, the social housing division of Morgan Sindall, boosting turnover £80m to £200m a year.
This is Morgan Sindall's second acquisition in less than a week, following its purchase of Miller's civil engineering division for £20m last Friday. John Morgan, chairman of Morgan Sindall, said Carillion's strengths in refurbishment, PFI and regional coverage would strengthen Lovell.
He said: "It will accelerate the development of Lovell to become the most accomplished social housing specialist in the UK. We see a big growth – and a good future in social housing."
Morgan would not reveal how much he would pay for the business, saying that would depend on how the deal was structured.
It is expected that Morgan Sindall will take on the 400 staff and the bulk of the workload. It will not buy the repair side of the business.
Morgan said Carillion's social housing was "in the black" but "not hugely profitable". Lovell's turnover last year was £108m, with an operating profit of £2.7m.
On the Miller Civil Engineering Services purchase, Morgan said managing director Graham Grundon would continue to run the business as a separate division within Morgan Sindall.
The Rugby-based company, which has a turnover of £135m and 650 staff, is one of the country's biggest tunnelling contractors. Clients include utility companies such as Anglian Water and Thames Water.
It also operates in the road, rail and air sectors and offers outsourcing services from design to operation for utility companies.
The sale leaves Miller, one of the UK's largest privately owned contractors, free to focus on its core housebuilding, property and construction interests.