The £250m revenue property services business could fetch up to £30m, according to city sources.
News of a potential major disposal comes after last week’s decision by Kier chief executive Haydn Mursell to step down immediately.
This followed Kier’s poorly received £250m emergency rescue rights issue, which left its banks forced to mop up £164m of underwritten stock and pressure from a major shareholder for him to step down.
The cash raising helped to reduce calendar year-end net debt to £130m, compared with £239m at the end of the previous year.
Kier’s board has now said it is on track to achieve a net cash position at its year-end in June 2019, but also warned that better trading would be weighted towards the second half of the financial year.
Despite flagging up plans over a year ago for disposals to strengthen its balance sheet, the only significant deal so far has been to sell a stake in Australian road assets and management services business KHSA for £24m.
Previous to this, Kier sold its third-party pension management business for £3.5m.
The housing maintenance business forms part of the Kier Services division, which also includes its waste collection and highways maintenance activities.
Kier has also been exiting waste collection contracts with local councils as it seeks to reduce its exposure to the sector.
In the latest move, Torbay Borough Council is expected to agree a plan to set up a company to replace a joint venture with Kier, which would make it the sixth council in a month to end ties with the firm.
Last week Cheshire West & Chester Council agreed to establish a council-owned company for waste collection after Kier said it would not seek to extend the contract.