Unions are pressing a Scottish council not to award a contract to any firm found to have blacklisted construction workers.
Dundee City Council is set to decide which company will build a new multimillion-pound museum in the city.
Unions say that building firm BAM should be excluded from the work because it has blacklisted workers - a claim denied by the company.
Steve Murphy, general secretary of the building workers' union Ucatt, said: "Until blacklisters fairly compensate the workers whose lives they ruined, they should be banned from public contracts.
"The Scottish Government is introducing clear guidelines to penalise blacklisters and Dundee Council must respect those rules."
The blacklist was discovered five years ago after a raid by the Information Commissioner's Office (ICO) on The Consulting Association (TCA), which compiled the names of more than 3,000 mainly building workers.
A spokesman for BAM Construction said: "We can say categorically that BAM Construction in Scotland did not use the services of The Consulting Association nor engage in any activities relating to blacklisting.
"We confirm that BAM Construction in other parts of the UK used the referral services of TCA to a very limited degree and all such usage ceased completely in 1998 when the UK Data Protection Act was passed.
"The company has accounted for this, apologised, put appropriate procedures and training in place to prevent any such occurrence in the future, and has given a public commitment to compensate fairly anyone who can show they have suffered any detriment because of BAM's historical involvement with the TCA."
A Dundee City Council spokesperson said: "All contractors working for Dundee City Council have to demonstrate that they meet the Scottish Government's policy regarding any involvement in blacklisting."
Meanwhile, the ICO has denied union claims that it is refusing to hand over details of workers whose names were on the blacklist.
The organisation said it was objecting to a court application by the GMB for up-to-date contact information it holds.
A spokesman said: "We don't hold up-to-date contact information for all those listed on the blacklist. We hold the original list, which we have already provided to the GMB.
"The contact details on that are more than five years old, and are incomplete in many cases.
"Last year we worked with the Department for Work and Pensions to get contact details for those individuals on the list who had a national insurance number listed.
"This gave us addresses for fewer than half of those on the list, and we subsequently wrote to those people.
"We were given the contact details expressly for this purpose and not for passing on to GMB. Our letter included GMB's contact details, so anyone who wished to speak to the union about the blacklist has had the opportunity to do so.
"We also hold contact details (though not necessarily up-to-date details) for around 500 individuals who have contacted us directly and learned they were included on the blacklist.
"These individuals are all aware they are on the blacklist and have a copy of the record held about them. None of these individuals were asked for their permission to pass their information on to third parties, including trade unions."
Justin Bowden, national officer of the GMB, said: "Dundee provides a focus today for the wider campaign to get justice for everybody who was blacklisted. We expect every company guilty of blacklisting to own up, clean up and pay up."
Shadow business secretary Chuka Umunna told the TUC Congress in Liverpool that the next Labour government would launch a public inquiry into the " inexcusable" blacklisting of workers and end the practice once and for all.
He told delegates he was open to the issue of whether blacklisting should be a criminal offence, but did not want to prejudge the inquiry.