Trinity announced earlier this month that it would close the plant, moving its North West portfolio, which includes the Liverpool Echo and Liverpool Post, to its Oldham site.
However, the move has been met with criticism from Unite, which has separately raised concerns over the increase in supersite contract printing in the UK.
Tomorrow (20 September) from 11am, Unite members from the site will appeal to local people to support their bid to keep the newspapers printed in the city.
Trinity employees will be talking to the general public in the city centre about what the newspapers, which have been printed in the city for 150 years, mean to Liverpool.
As part of the campaign, the union has organised a petition that calls on the local community, government and MPs to voice their support for the Liverpool print site.
Unite Regional Officer Paul Finegan said: "Too many highly skilled jobs have already been lost on Merseyside and we will not stand by and let Trinity Mirror move the printing of its local newspapers out of this city without a fight.
"Liverpool is a city with enormous pride and more than 150 years of printing production history. A city celebrating its achievement of Capital of Culture and a bright future ahead that deserves to have its own print and distribution operation at the heart of its readership.
"It's time the company listened to its readers' concerns and redirected its investment in Liverpool to protect the future of the workforce."
He urged Trinity Mirror to have "meaningful talks" with the union to examine "every possibility" to retain production on Merseyside.
However, Liverpool Echo editor Ali Machray has defended Trinity Mirror Printing's decision to close its Liverpool plant, citing anticipated expansion costs of £28m-plus that would result in "commercial suicide" for the newspaper.
Unite to petition against Trinity Mirror's move out of Liverpool
Unite has launched a campaign to stop Trinity Mirror's plans to relocate its Liverpool print site to Greater Manchester.