The site currently employs 58 staff, it is unclear if all would lose their jobs in the proposed closure of the site, which prints the Grimsby Telegraph, the Scunthorpe Telegraph, the Lincolnshire Echo and the Hull Daily Mail.
Staff at the site are employed by Harmsworth Printing – the regional printing arm of Associated Newspapers and DMGT.
Peter Williams, finance director of DMGT, said the move was a result of surplus capacity: "The need to balance capacity with contracts is a challenge facing the industry as a whole.
"We need to ensure that our presses are utilised efficiently at all times of the week."
The news came as DMGT revealed its overall total revenues in its Northcliffe Media local newspaper division were down 5% compared to the same period last year.
This exacerbated a 3% fall, recorded by Associated Newspapers, which counts the Daily Mail among its titles, in July and August.
Williams said the local newspaper advertising market was affected by the sectors it covered: "Advertising in local newspapers is dominated by property and recruitment; both markets have seen a downturn."
Williams said he had "no idea" how long the downturn would last but added that the company was "not hopeful" about the coming 12 months.
Grimsby is the third newspaper printing plant to face closure this month with Trinity Mirror set to close its Liverpool site and Newsquest planning to shut its Colchester plant.
Harmsworth's move will add more fuel to Unite's claims that newspaper supersites, particularly News International's Broxbourne plant, will lead to consolidation and widespread job losses.
Steve Sibbald, Unite national officer, said: "Northcliffe, along with Newsquest, is the most vulnerable because they have old presses. If there is any over-capacity, they consolidate.
"We understand that the printing will move to Leicester, I don't know whether the people of Grimsby will be happy with their newspaper being printed in Leicester. But it is inevitable that these little centres will go."
Print jobs at risk as Harmsworth proposes Grimsby site closure
The newspaper industry is bracing itself for further job losses with the announcement that a consultation period has begun at Harmsworth Printing's Grimsby site.