Mears heads the list of potential buyers with the Scottish division said to be attracting most enquiries.
Mike Jervis, partner and joint administrator at PricewaterhouseCoopers, axed 558 employees in maintenance and improvements, 82 in the construction business, 69 in the Scotland PHE (Plumbing, Heating and Electrical) division and two at the Exeter head office.
The job losses came as little surprise after the company plunged into administration on Monday owing 60 million to Royal Bank of Scotland, Clydesdale Bank and HSBC. It had issued a profits warning in August and it is thought some suppliers demanded early payment.
The company employed 3,800 across the UK, including more than 750 in Scotland. Work on a number of projects including the new bottling plant for Diageo in Fife and a number of contracts for Highlands & Islands Enterprise had to be suspended.
Jervis said: "Regrettably, the redundancies made today were necessary for economic reasons where there has been little or no interest in the business from prospective purchasers or where there was insufficient work for staff to carry out.
"In the case of the maintenance and improvements division, we are rationalising the national network to slim down areas where there is not enough work for employees, principally in the build division."
Jervis said: "We are working closely with employees affected by this decision to ensure they receive the support they need to assist with their claims for redundancy and other compensatory payments. Staff affected by this will be paid up to and including today.
"On a positive note, we have had over 100 expressions of interest in the business and we are currently reducing this to a shortlist.
"There are still national contractors interested in all divisions, as well as parties interested in individual divisions.
"We are short-listing bidders on the basis of their size, level of interest in acquiring large parts of the business and their speed of reaction. We expect to have further updates by the end of the week."