Administrator PricewaterhouseCoopers is looking to seal a deal quickly in a bid to save as many of the 3,800 jobs as possible.
Mears is looking to snap-up all of Rok’s social housing contracts. Leadbitter and Kinetics are also believed to be in the hunt.
Rok’s social housing contracts look likely to be sold en masse while its string of smaller building jobs will be bought on a piecemeal basis.
Mike Jervis, joint administrator and partner at PwC said: “Our immediate priority is to urgently review the financial position of the company and seek a buyer of the businesses.
“We will work with the existing management team, employees, suppliers and customers to try and ensure that we achieve a positive solution.”
Mears chairman Bob Holt said: “We’re waiting to hear from the administrator and waiting to get access to information. That will probably be in the next 24 hours.
“Negotiations could take another 24 hours. We hope to have deals done by the end of week.”
Latest results for Rok for the six months to August 31 show the firm made a £3.8m pre-tax loss on a turnover of £308m. Maintenance work accounted for £116m of turnover, social housing £84.5m and construction £116m.