Demonstrators organised by the Unite union plan to protest outside the site on Friday.
The union said the site was being targeted because sister company Bam Nuttall was one of more than 40 firms who used the services of the Consulting Association which disbanded in 2009.
Martin Rogers, Executive Board Director, Royal BAM Group, said: “Blacklisting has no place in today’s construction industry.
“We have fully cooperated with the investigation carried out by the Information Commissioner’s Office (ICO) in 2009 and at that time no action was taken.”
Unite general secretary, Len McCluskey said: “Manchester City fans deserve to know that BAM the company redeveloping the club is a known blacklister.”