One boss at a major contractor said the firm had formed a team to snap up disgruntled workers among the 1800 employed by the division.
He said: "Everybody is after Laing staff. I am sure that headhunters will be approaching them."
Laing construction directors have reacted to the danger by offering senior staff incentives to stay until the business' sale is completed, which is expected to be early next year. This has lessened the chances of a management buyout, which was mooted by some sources in the immediate aftermath of the announcement.
Recruitment consultants have confirmed that they have received approaches from Laing staff, mainly from less experienced staff.
One consultant in the North-east said 12 staff had approached him, mainly project and site managers. He said: "The fear is that if the firm is bought by another contractor there will be redundancies. People with three or four years' experience are registering because they will not get as generous a redundancy package as employees who have been with the firm for 15 years."
Another consultant said many staff had no need to go to recruitment agencies as the firm's reputation was good and they would be signed up by Laing's rivals.
No front runner to buy the Laing division has emerged, although speculation surrounds Swiss contractors Batigroup and Zschokke.
Everybody is after Laing staff. I am sure the headhunters will be approaching them
Other candidates include Swedish firm NCC and Australian outfits Multiplex and Westfield.
One homegrown contractor said UK groups would start to look at the construction arm if a deal was not reached with a European firm, the option favoured by Laing. He said: "There would not be as much price competition."
This has raised concern that the sale could drag on and lower staff morale, already dealt a blow by last month's shock announcement.
A Laing spokesman moved to allay staff fears and stressed that there had not been any haemorrhaging of staff since the sale announcement.
The spokesman said: "There are a lot of good opportunities at Laing. Once the period of uncertainty is over there will be positive and exciting opportunities."
One source close to Laing said there was considerable anger at the handling of the sale.
The source said: "Staff say they feel rejected and betrayed. They feel like children being thrown out of their house by their parents."