Five Eyes is an intelligence alliance between New Zealand, Australia, Canada, the United Kingdom and the United States.
Earlier today during Question Time, Bridges claimed that the GCSB had given assurances to Five Eyes partners that the Treasury had not been hacked.
"Did the GCSB raise with the Government that Five Eyes members had raised concerns regarding the systematic and deliberate hack?" Bridges asked.
Deputy Prime Minister Winston Peters, answering on behalf of the Prime Minister, said he was "not aware of that".
"But I do not think that Five Eyes were struggling over themselves on a matter to do with Treasury. With the greatest respect, it's not foreign policy, it's not police, it's not defence, it's not customs—it's Treasury, and I find it very hard to believe that."
After Question Time,a spokeswoman for Bridges would not reveal the basis of his claim, but said there were "multiple reliable sources".
The spokeswoman would not say which partners had contacted the GCSB, but said "at least two" had done so.
"That's when the GCSB contacted Ministers to tell them not to use the term 'hack', because they had Five Eyes partners calling," the spokeswoman said.
But Hampton said that Five Eyes partners had not raised any concerns.
"The GCSB has a long-standing practice of not commenting on its engagement with its intelligence partners for reasons of national security.
"However, due to the need for clarity regarding the Treasury incident, I can confirm that Five Eyes partners have not raised concerns with me directly or with my agency."
He added that the contact was operational and Ministers are not required to be briefed.
Peters, who is also Foreign Minister, also said during Question Time that the Ministry of Foreign Affairs and Trade did not become involved in the contact with Five Eyes members about the so-called hack.
"There is no way that such an involvement of foreign affairs would've happened without the Minister of Foreign Affairs knowing. Being asleep behind the wheel is not what the present Minister of Foreign Affairs does."
Earlier today National deputy leader Paula Bennett challenged Prime Minister Jacinda Ardern's claim that the GCSB had wanted to describe what had happened as "unauthorised access" instead of "hacking".
While at a parliamentary select committee, Bennett said that the GCSB had told the Treasury that its preferred description was "information management issue".
But a spokesman for Ardern said that the GCSB had "clearly" told the Prime Minister's office to use "unauthorised access".
He added that he could not speak for conversations that may have happened between the Treasury and the GCSB.