The company, which has been owned by asset management group Henderson since 2006, is expected to raise tens of millions of pounds if it successfully completes its listing, Sky News reported.
RBC is advising John Laing on the flotation and HSBC and Barclays are acting as book runners for the deal.
The possibility of the company being sold off by Henderson first surfaced in 2010, when the group floated its infrastructure fund. The firm’s management was forced to deny that the group itself was seeking a new listing worth £60m at the same time.
John Laing built Cardiff’s Millennium Stadium, a project which partly contributed to the firm selling its construction arm after costs spiralled out of control. More recently, the company worked on the new Alder Hey Children’s Hospital in Liverpool.
The company declined to comment yesterday.