Carillion was this week in talks with Australian companies, known to include Bovis Lend Lease, to sell Mowlem's Australian business Barclay Mowlem.
Carillion is looking to offload the business, thought to be worth between A$150m and A$200m (£61-81m), because it has no other interests in Australia.
A source this week said the talks, which come less than a month after Carillion completed its £313m takeover of Mowlem, were at an early stage.
Barclay Mowlem, which numbers furniture chain Ikea among its clients, employs more than 2000 people and has an order book of A$900m.
News of the talks will come as little surprise to the City. When Carillion bought Mowlem chief executive John McDonough said all the Mowlem businesses would be rebranded except Barclay Mowlem and cleaning firm Mowlem Pall Mall. Neither was considered a good fit with the rest of the business.
Finance director Chris Girling, who flew to Australia immediately after the takeover, said earlier this month that Carillion had identified a number of Mowlem businesses that would be reviewed. He added: "Everything is for sale at the right price."
Developer Lend Lease is known to be in discussions with Carillion over Barclay Mowlem, and is understood to have appointed Deloitte to handle the negotiations. If a deal goes ahead, Barclay Mowlem would be subsumed within Lend Lease's construction arm. Bovis. Bovis Lend Lease and Carillion declined to comment this week.
When Carillion's results were released earlier this month, Girling said it could not guarantee there would be no more write-downs on Mowlem. Carillion has already written off £45m on Mowlem contracts and £75m on its assets.