Consultation at the £17m Bolton plant, which only opened in 2001, began on Wednesday 3 December and will be concluded on 5 January next year.
The news follows the announcement in September that the company was to begin a consultation into its Colchester plant, resulting in 80 redundancies.
Currently around 80 staff are employed at the Wingate site, which prints several north west newspapers including the Bolton Evening News and Lancashire Evening Telegraph.
A statement to employees from regional managing director Chris Hughes said the proposal to close the plant was in response to extremely tough trading conditions and the expectation of revenue continuing to fall in 2009.
He said: "The company believes it can print all weekly titles at other print plants within Newsquest. The two daily titles would need to be printed outside of the group.
"Conversations have been held with North Wales Newspapers, which operates a press in Flintshire.
"Conditions during 2008 have deteriorated dramatically as the year has progressed. Paginations are down significantly."
He added: "It is expected that 2009 will continue to be a very challenging period for the company and it is therefore essential that all possible efficiency savings be considered."
However, Unite said that the move was badly thought out by Newsquest.
Paul Finegan, national officer at Unite, said: "I think publishers need to think more about logistics.
"They are talking about printing the titles in North Wales or even Glasgow. It could be a logistical nightmare and it will get to the point where local people won't buy local newspapers any more."
Newsquest begins consultation over print site closure
Newspaper publisher Newsquest has begun a consultation to close another of its print sites in the New Year.