The families of the two Romanian men said they would be taking legal action against the paper after the Crown Prosecution Service decided last week that its key witness was unreliable.
Adrian Pasareanu, 27; Alin Turcu, 18; Luzim Balliu, 30, and two others who cannot be named for legal reasons were arrested by police after an undercover investigation by the newspaper.
The News of the World claimed they had been planning to kidnap Ms Beckham and her children outside the family home in Hertfordshire and hold them to ransom. But the case collapsed on Monday after the CPS accepted that Florim Gashi, who had accepted £10,000 from the paper for a tip-off and who had previous convictions for dishonesty, was an unreliable witness.
The father of Mr Pasareanu said that his son, a medical student, would sue the newspaper for libel. He told the Media Guardian website: “Adrian told me that while he was at a party in London one of the guests started a conversation about how to make money without working and the name of Victoria Beckham was mentioned. Someone recorded the conversation and got £10,000 for the tape.”