The company has been locked in talks with Tata Steel over the purchase of Tata's Clydebridge and Dalzell works.
Tata Steel announced in October it would close them with the loss of 270 jobs.
However, Liberty said that while a deal was close, talks may not be concluded on Wednesday.
It is understood that the question of responsibility for any future clean-up costs has still to be resolved.
The Scottish government has been involved in negotiations, as has the UK government.
Liberty House plans to use the Scottish mills to turn re-cycled steel into steel plates for use in construction and motor manufacture.
The company hopes to process about two million tonnes of scrapped steel a year, rather than melting new steel.
It estimates about 12 million tonnes of steel are scrapped in the UK every year.
But the company says that is dependent on negotiating an energy regime which makes the process sustainable.
It is holding talks with the Westminster government on offsetting the carbon tax for large scale energy users and/or improving the feed-in-tariff for surplus power from its renewable generation.
Earlier Ms Sturgeon said "final due diligence" on an agreement was taking place.
She told MSPs: "The agreement would be facilitated by the Scottish government and would involve us buying the plant and immediately selling them on to Liberty for the same consideration."
The announcement came ahead of a meeting of the Scottish steel task force, set up by the Scottish government in October to try to secure a future for the mills.
Roy Rickhuss, general secretary of the steelworkers' union Community, welcomed news that a deal was close.
He added: "The signing of this agreement is the first step towards restoring jobs and resuming production but there are still many steps to be taken.
"Community will continue to work tirelessly to see that happen.
"We made it clear that the skilled workforce at Dalzell and Clydebridge deserved a future in steel and from my discussions with Liberty I know they have the ambition to make that happen."
International metals firm Liberty House has confirmed that a deal to buy two mothballed Lanarkshire steelworks is close.