The steel giant, owned by GFG Alliance and magnate Sanjeev Gupta, owns both the Dalzell and Clydebridge steel plants in Scotland.
It has been reported a winding-up petition against the specialty steels division of Liberty Steel was filed this week and is expected to be heard late next month.
It is not known how much the business owes HMRC, but reports suggest it is in the tens of millions of pounds.
If it leads to the collapse of the business, it could lead to the loss of hundreds of jobs at the Scottish plants.
The details follow the revelation the Scottish Government may have broken state aid rules as part of its involvement with the sale of Dalzell steelworks to Liberty Steel in 2016.
Ministers owned the plant it had bought for £1 for mere moments as it brokered a ‘back-to-back’ sale from TATA to Liberty.
The Government also agreed an indemnity clause during the deal that passed on the liability for future clean-up costs from Tata, to the Government, and on to Liberty Steel.
It was this clause business minister Ivan McKee said may have breached state aid rules, potentially leaving the Scottish Government with the liability if Liberty Steel collapses.
However, Mr McKee claimed in his statement to Parliament this means the indemnity clause is “unenforceable”, though Tata said they believed the clause was still “valid and binding in all aspects”.
It is not yet known whether the winding-up petition from HMRC will lead to the collapse of Liberty Steel or see further financial liabilities for the Scottish Government.
Liberal Democrat economy spokesperson Willie Rennie said the news required “urgent clarification”.
He said: “I am very anxious about what this could mean for the jobs at Liberty Steel’s plants at Dalzell and Clydebridge.
“The workers at the plant are dedicated and don’t deserve to be caught up in the financial swamp of GFG Alliance.
“We need urgent clarification from the Scottish Government as to what this could mean for the employees.
“We also need clarity on what this could mean for taxpayers as a result of the disputed multi-million pound guarantee which the Scottish Government signed to facilitate the sale of the plants to Liberty Steel, part of the GFG Alliance.”
Richard Leonard, the Scottish Labour MSP, said an urgent statement to Parliament was required following the announcement of the winding-up petition.
He said: “This is a major concern and shows why more transparency is needed.
"It is in the public interest, and the interests of the workers at Motherwell, Clydebridge and Lochaber, that the Scottish Government publishes details of all the deals it has done with this company.
"Ministers must make an urgent statement about its financial exposure to GFG and the Guptas."
A Liberty Steel spokesperson said: "Our priority has been to protect thousands of jobs in the UK.
"We are committed to repaying all our creditors and continue to work with all stakeholders around the UK to create a sustainable future for our businesses following the collapse of Greensill Capital.
"Against a very challenging backdrop in the UK with record high energy prices and imports, we have provided tens of millions in funding to keep our people in employment and maintain operations to serve customers and strategic supply chains while we complete our refinancing.
"We are in continuous dialogue with all our creditors, including HMRC, to find an amicable solution that's in the best interest of all stakeholders.
"Short-term actions that risk destabilising these efforts are not in anyone's interest, and undermine creditor recovery at a critical stage in our debt restructuring efforts that seek to secure the future of our businesses."
A Scottish Government spokesperson said: “We are aware of the winding-up petitions brought by HMRC against a number of English-based Liberty Steel UK businesses. No such action has been brought against Liberty Steel Dalzell. However, we are engaging with the business to understand any potential impact these winding up orders may have on Liberty Steel Dalzell and the wider group.
“As ministers have previously stated, the Scottish Government has no liabilities in respect of the steel plants at Dalzell and Clydebridge.
“Our intervention in 2016 enabled Liberty Steel to operate the Dalzell steelworks, retaining heavy steel plate production in Lanarkshire and saving more than 100 jobs.”