The decision to sell was partly triggered by "unsolicited approaches from a number of parties" looking to buy parts of the company including the "very successful" Australian business, Laing O'Rourke said.
The company said it will now focus on growing its business in Europe and the UK in particular. Its European business is "very well placed for strong growth potential" and in the UK "will be further fuelled by the government's renewed focus on infrastructure and new housing", it said.
The company is believed to be looking for over $1 billion for the Australian business, Australian Financial Review said.
The sale will be led by HSBC investment bank, Laing O'Rourke said.
In its 2015 annual review Laing O'Rourke said it had built up a "diverse portfolio spanning the oil and gas, transport, building construction, defense, airports, mining, marine and civil, and social infrastructure sectors" in Australia, where it began operating in 2004. Since acquiring Australian infrastructure firm Barclay Bowlem in 2006, Laing O'Rourke has grown to become the largest privately owned engineering and construction business in Australia, it said.
However, it warned that 2014 had "marked a year of negative real growth in the Australian construction sector as the resources boom subsided, utilities construction entered a downturn, and government fiscal policy tightened, coupled with a weak commercial sector".
"Most economists expect a period of downturn extending into 2017, principally driven by a 30 to 40% decline in resources construction. The largest falls occurred in oil and gas, which was the sector that had enjoyed the biggest upturn through the record-spending schemes of previous years," Laing O'Rourke said in the report.
Laing O'Rourke's Australian business reported revenue of AU$2.7 billion ($1.9 billion) in 2014/15.