Remontowa was one of six shipyards to bid for a contract to build two new Caledonian MacBrayne ferries, but lost out to Ferguson Marine, the last commercial shipbuilder on the Clyde.
A BBC Scotland documentary last week raised multiple questions about the procurement process, with a leaked dossier indicating that the Inverclyde-based firm benefited from preferential treatment.
One expert report submitted by CalMac during the tender process found that the bid from Remontowa best met its requirements.
The ferries are still under construction, but last week, The Scotsman revealed that further delays have beset the project, with total costs spiralling to around £300m.
The Scottish Government-owned ferry owner, Caledonian Maritime Assets Limited, which placed the order, rejected claims there had been "preferential treatment" offered to Ferguson Marine.
First Minister Nicola Sturgeon also told Holyrood that she had not seen any evidence of criminality in the procurement and construction of the ferries, but insisted coming to that conclusion was “not my job.”
However, her deputy, John Swinney, confirmed to MSPs that Auditor General Stephen Boyle is to look into the 2014 procurement process with the full support of Scotland’s most senior civil servant, John-Paul Marks.
Now, Remontowa, which previously built three CalMac ferries, has signalled that it could be set to take legal action over the deal.
A spokesman for the Gdansk-based company told the Scottish Mail on Sunday that the situation was a “serious matter.”
He said: “We are investigating the matter. Our legal team realises the tender might have been fraught with irregularities.
“Much depends on whether the irregularities made public are confirmed. At the moment, our lawyers are analysing the situation to consider possible formal steps, but no binding decisions have yet been taken.
“We must carefully weigh up the pros and cons. This is a very serious matter and so will be the decision that must be taken at the highest level in our group.”
Douglas Ross, leader of the Scottish Conservatives, warned that any legal action would hit the public purse.
He said: “The SNP's deal in awarding Ferguson's this contract was clearly rigged. 'Their cover-up and secrecy surrounding the deal could now land taxpayers with an even greater bill, if this legal action comes to pass.
“We know from the SNP's embarrassing attempt to redact crucial documents that could in fact still be read, that a legal challenge like this could even render the contract ineffective.
“Taxpayers are paying the price for this fiasco and it is time ministers, including Nicola Sturgeon herself accepted responsibility for their catastrophic errors.”
A spokesman for the Scottish Government said: “Ministers are not aware of any impropriety in the procurement process, but take the claims made in the BBC documentary extremely seriously and will explore what further steps the government needs to take to ensure that all questions about the fairness and appropriateness of the tendering process are properly, independently investigated.
“The permanent secretary, at the request of ministers, has already proactively been in contact with the Auditor General to discuss this matter.”