BAM has been contracted by MCFC to carry out the £100 million redevelopment of the training ground.
Union group, Unite said it is is "convinced the company has been involved in the blacklisting and victimisation of trade unionists working on Crossrail, Europe's biggest construction project".
"Blacklisting ruins lives and we believe it is continuing today on Crossrail because of contractors like BAM," Unite general secretary, Len McCluskey, said.
"Manchester City fans deserve to know that BAM the company redeveloping the club is a known 'blacklister'.
"It is ruining the lives of ordinary construction workers. BAM's reputation is at serious risk and it's embarrassing its clients. Unite will use every legal means to end this blight and to expose the companies and individuals that indulge in blacklisting," McCluskey added.
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."
