The two plants were mothballed after owner Tata Steel announced 1,200 jobs cuts in October.
225 jobs were lost at the Dalzell plate rolling works in Motherwell while 45 posts were cut at the Clydebridge plant in Cambuslang.
Elsewhere, a further 900 positions were lost at Tata's facility in Scunthorpe.
The firm blamed the cuts on a flood of cheap imports from China, a strong pound and high electricity costs.
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It is understood international metals firm, Liberty House, is now interested in acquiring the Dalzell and Clydebridge works.
Speaking after the fifth meeting of the Scottish Steel Task Force, Business Minister Fergus Ewing said: "The Task Force welcomed the interest of Liberty Group and agreed it was a positive step in our objective to keep the Dalzell and Clydebridge plants open. While nothing is yet agreed, there is a degree of optimism at the current situation.
"Time is of the essence and the Scottish Government and Scottish Enterprise can offer support to any new commercial operator wishing to restart operations, with action being taken forward on energy costs, business rates, procurement and on environmental issues.
"All members of the Task Force will continue to do everything possible to secure a sustainable future for Scottish steel."
(LM)
