Under the proposals, three older presses will be taken out of action, leading to the loss of up to half of the 380 jobs at the Scarborough plant.
The plant's finishing department will remain open under the plans, which were revealed to employees and Unite, the union, today.
The future of Greaves has been in doubt for several years following the opening of Polestar's gravure superplant in Sheffield. The group also closed its Purnell gravure site in 2005. Other than the Sheffield site, Polestar's only other remaining gravure plant is Varnicoat in Pershore, Worcestershire.
Barry Hibbert, Polestar chief executive, said: "Polestar will effectively take three older presses out of production and maximise the efficiency of its greenfield facility in Sheffield and its firepower at Varnicoat.
"This action also recognises that there is too much print capacity in Europe and Polestar has been prepared to take a lead on this. For the sake of the market I hope other printers will do the same."
Unite national officer Vernon Robson said: "This is another blow for manufacturing, the print industry and our members in Scarborough. These are some of the best paid jobs in the Scarborough area and will be difficult to replace.
"We will be meeting with our union officials immediately to determine our response to the proposed closure and we will seek urgent meetings with the management to minimise job losses."
Greaves produces magazines and newspaper supplements including Hello!, Woman's Weekly for IPC Media, Stella for The Telegraph, Take 5 and S Magazine for Express Newspapers and Life for The Independent.
190 jobs at risk as Polestar plans closure of Greaves printing operation
Polestar has announced plans to close the print department of Greaves, its ageing gravure plant, and urged other printers to take further capacity out of the long-run print market.