Staff at the Sussex site, which is responsible for printing The Argus, as well as a number of free weekly papers, have entered into a 30-day consultation, with printing of the local paper expected to move to the company's Southampton print facility.
Steve Sibbald, national officer at Unite, confirmed it would begin talks with Newsquest in an attempt to retain printing at the site.
The proposal comes little more than a year since 27 pre-press jobs at its Brighton and Swindon sites were axed with the positions outsourced to India.
Last year also saw the closure of its Colchester print plant, which prints the Essex County Standard and the Colchester Gazette.
Should the Brighton site be closed, Newsquest will have seven plants across the UK.