The Direct division previously included the Crayford plant which closed last year.
It is understood that a consultation will begin on Monday (17 May) and Unite officials are planning to meet with the company next week.
Unite assistant general secretary Tony Burke said: "This is another body blow in terms of job losses in the print industry and we are very concerned about the closure."
It is unclear at this stage what St Ives' intentions are and the company was unavailable for comment. However, PrintWeek understands that there may be plans to move one or more of Edenbridge's presses to other St Ives facilities.
Unite regional officer Tim Elliott is heading up Unite's efforts at the Kent plant, which suffered an explosion just under a year ago.
He said: "We will try to keep the plant open but, if it does close, we will certainly look to relocate as many people as possible, which the company has done in the past."
St Ives Direct still has facilities in Leeds, Blackburn and Bradford.