Hinton, who was one of Rupert Murdoch's closest lieutenants at News Corp until he resigned in July, said that he "had no reason to believe" that Goodman's claim was accurate, or that there was any "evidence" to support his allegations.
In a letter submitted to the Commons culture, media and sport select committee, Hinton also said that he stands by the evidence he gave to the MPs in 2007 and 2009, in which he expressed his belief that Goodman was "the only person" involved in phone hacking at the News of the World.
Last month, the culture committee published a letter sent by Goodman in 2007, in which the reporter said that he was promised he "could come back to a job at the newspaper" if he "did not implicate the paper or any of its staff" in his mitigation plea.
Goodman also crucially claimed that phone hacking was "widely discussed" at News of the World editorial meetings chaired by the then editor Andy Coulson.
Discussing the claims, Hinton said: "As for Mr Goodman's assertion that he had been promised he could come back to a job at the newspaper 'if [he] did not implicate the paper or any of its staff in [his] mitigation plea'.
"I had no reason to believe that his allegation was accurate, and am not aware of any evidence to support it. Accordingly, I testified before the committee in 2009, no evidence was provided to me that the conduct of Mr Goodman had spread beyond him."
Earlier in the week, former News of the World legal manager Tom Crone said at a select committee hearing that Coulson was keen to re-hire Goodman even if he was jailed for phone hacking offences.
Crone and former News of the World editor Colin Myler also told MPs that they were "certain" James Murdoch knew about a key email, which suggested that knowledge of phone hacking at the paper went beyond one "rogue reporter".