The group has emerged as a potential buyer for the Dalzell and Clydebridge works, according to the BBC.
The Scottish Government's steel taskforce is meeting later to discuss the future of the plants, which support 270 jobs.
Efforts are continuing to secure a new commercial operator, with a possible deal with Greybull Capital emerging last month.
Fergus Ewing said: "Liberty House has a proven track record in the UK steel industry and this is a welcome development in the quest to secure a sustainable future for Scottish steel.
"I met Liberty management last week to outline the range of potential support that would be available from the Scottish Government and Scottish Enterprise should it succeed in a buyout.
"I also emphasised that the Scottish steel taskforce continues to work constructively to ensure a viable future for the plants, with action being taken forward on energy costs, business rates, procurement and on environmental issues.
"The steel taskforce will meet this morning and reflect on this positive development."
A support package of £195,000 to retain key staff at the plants in Motherwell and Cambuslang has been agreed by ministers.
A number of employees will be paid about 60% of gross salary and receive advanced training to ensure the sites can reopen quickly as and when production resumes, the Scottish Government said.
Tata announced 1,200 UK job losses in October.