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.

The small objects were hidden by artist Luke Jerram for his installation Treasure City, with clues hidden in paintings at the 20-21 Arts Centre.
The first one, a replica Viking brooch, was found in a wall in Kingsway Gardens, Scunthorpe, by Rachel Welch.
Ms Welch, of Grimsby, said she looked around town on the off-chance she could find one without cracking the codes.
The object was found hours after the treasure hunt began on Saturday.
She said: "We had a look at them, but we didn't really spend much time with them because we are no good at codes.
"We thought we'd go out and have a look round and see if we are able to find one and we did."
Bristol-based artist Mr Jerram said a Scoutmaster had cracked the code in the corresponding painting moments before, and arrived at the park to see it had already been claimed.
This particular artwork used semaphore to spell out the clue "in the gardens seven metres from the flag is the Kingsway xx(rest)."
The gold was hidden in a dry stone wall near a flag, given to the gardens as an environmental award.
Each of the objects is worth more than £1,000 and Ms Welch said she was going to sell it to pay for a holiday.
The second object, a small 18 carat gold lamb, was found in a bandstand in Brigg on Sunday night by a teacher from Beverley. She solved one of the painting's codes to lead her to a place which was "an octagonal place to listen".
Mr Jerram said the woman searched Scunthorpe for somewhere that fit that description and settled on the bandstand but when she got to the one in Scunthorpe there was nothing there.
It was that night that she realised there was one in nearby Brigg and went down there with her husband at midnight to claim the gold.
The third piece, a model of a Tudor fisherwoman, was found on Monday but the exact details of where are not yet known.

Oxfordshire County Council has joined forces with new operator HourBike Ltd to bring back the OxonBike scheme, which has 30 cycles available to hire from seven locations around Headington.
The Â£150,000 project was originally launched in June last year, but the two-year pilot was cut short five months later when operator Grand Scheme Bike Share went into liquidation.
Hourbike will run it for a year.
David Nimmo Smith, the county's cabinet member for transport, said: "When the scheme launched last year around 500 people signed up, so I am sure that those people will be very keen to get back in the saddle.
"Commuters who use Thornhill Park and Ride and who travel in and around Headington to places like the universities and hospitals will find OXONBIKE particularly useful."
The cost of hiring the bikes is free for the first 30 minutes.
The scheme has been funded by the government through its Local Sustainable Transport Fund.
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.
[NEXT_CONCEPT]
Three of five gold artworks hidden in Lincolnshire as part of a treasure hunt have been found - the first by chance.
[NEXT_CONCEPT]
A bike hire scheme has been relaunched in Oxford six months after it folded.