Ex-Bank of England deputy governor Sir Charlie Bean is reviewing how official statistics are collected, and his initial findings are due on Wednesday.
The PCS union said it would "strongly oppose" transferring work or jobs from Newport, where 2,000 staff are based
The ONS said it was not "helpful" to speculate on the report's findings.
The ONS transferred hundreds of jobs from London to Newport in the late 2000s.
PCS union representative Gez Kirby said: "There's some anxiety obviously."
He told the BBC's Sunday Politics Wales programme: "We believe we produce high quality economic statistics and we don't want to see any of our work or our jobs move out of Newport."
Mr Kirby added: "We welcome any recommendation coming from the Bean Review, to increase the economic expertise in London, because they can liaise with the Treasury, the Bank of England, that makes sense.
"We would not welcome, and we would strongly oppose any proposal to transfer work or jobs from Newport."
Sir Charlie has previously said the ONS is "maybe not quite such a strong performer" as it once was.
However, more recently, he also said Newport could become a centre of expertise in the field of statistics.
An ONS spokesperson said: "ONS has welcomed the Bean Review as a good opportunity to review our systems and processes for measuring the changing UK economy."
"As the interim report of the review is due to be published shortly, it would not be helpful to speculate about its content.
"We look forward to reading its recommendations when it is published."
Sunday Politics Wales can be seen on BBC One Wales at 11:00 GMT on 29 November.
Office for National Statistics (ONS) staff in Newport are anxious that a government review will lead to jobs leaving south Wales, a union has said.