On Monday, Liberal Democrat MP John Hemming publicly named former Wales player Giggs as the footballer who had taken out an injunction after allegations that he had an affair with ex-Big Brother star Imogen Thomas.
Ferguson did not realise that his comments were being recorded when he was overheard ordering a press officer to "ban him on Friday", referring to Rob Harris, a sports correspondent for the news agency Associated Press, who had asked the United manager "how important" Giggs was for the team ahead of Saturday's UEFA Champions League Final.
Clearly irritated, Ferguson replied curtly: "All the players are important, every one of them."
Moments later, the Scot was captured by a Sky News microphone asking press officer Karen Shotbolt about "the guy that asked the question about Giggsy…at the press conference".
Shobolt replied: "Which one?"
Shortly after, Ferguson is heard to ask: "Is he coming on Friday?"
Shobolt asked: "The guy with the laptop?"
Ferguson then ordered: "Aye. Then we'll get him. Ban him on Friday."
The incident draws parallels to the controversy during the 2010 general election campaign when Gordon Brown was caught on a Sky News mic calling pensioner Gillian Duffy a "bigoted woman".
Mark Evans, head of home news at Sky News, warned high-profile figures that "any microphone is a live microphone".
Lou Ferrara, the AP's managing editor of sport, added: "Rob Harris was doing his job as a journalist by asking a question. Our expectation is that he'll ask more questions and be afforded the ability to do so as he covers the world's most popular sport."
It is understood that Ferguson is unable to ban Harris from Friday's press conference as it is being organised by UEFA, meaning United has no jurisdiction over the event.
A spokesman for the Old Trafford club told BBC Sport: "I don't think we can [ban him], but check it out with UEFA. The answer is probably no."
Also yesterday, Greater Manchester Police confirmed that cars belonging to journalists and members of the paparazzi parked outside Giggs's home had been attacked by a group of masked men.