The facility, which prints York daily The Press and the North East's The Northern Echo, is in consultation to close, with 22 jobs at risk. The Press newspaper has been printed in York for 200 years.
Under the proposed plans, The Press will be moved to Newsquest's Bradford site, while The Northern Echo along with The Durham, Chester-le-Street and Consett and Stanley Advertisers will be printed at Teesside by Trinity Mirror.
The consultation is to close on 17 January 2009, a move which has angered Unite.
Unite national officer Steve Hart told PrintWeek: "It is never a good time to announce redundancies but for those people affected, over the holidays all they will be able to think about is their future, or the lack of it.
"If it were a couple of weeks before Christmas we could have sat down and talked about relocation plans, and had a few more answers.
"But a few days before Christmas doesn't leave us with any time. It is supposed to be a 30-day consultation, but we will definitely not have as much consultation as we would have liked."
Newsquest North East was unavailable for further comment.
Unite anger over Newsquest consultation to close York print site
Unite has hit out at Newsquest for the timing of its consultation into the closure of a newspaper print site in York.
