Liberty House is in negotiations to buy the Dalzell and Clydebridge facilities, which owners Tata intends to close.
The international metals business confirmed its interest to BBC Scotland this morning and said talks were at an early stage.
Tata blamed a combination of high energy costs and competition from cheap Chinese imports for its decision to end production at its Clydebridge plant in Cambuslang, where 65 jobs are going, and its Dalzell plate-rolling works in Motherwell, which could lose 225 staff.
Its decision to close the two plants effectively ended Scotland’s steel industry. A major plant in Scunthorpe, employing around 800, is also up for sale.
Tata previously signed a “Letter of Intent” in December with investment firm Greybull Capital for the possible sale of its Long Products business, including the Scottish mills in Dalzell and Clydebridge, as well as steelworks in Scunthorpe and Teesside.
But Community, a trade union representing staff at the Lanarkshire plants, said such a deal would not “solve the problem” of job losses.
First Minister Nicola Sturgeon announced the creation of task force in October to help identify a potential buyer for the sites.
She promised to leave “no stone unturned” in the Scottish Government’s efforts to secure a viable future for the industry.