In a statement, the company said the decision to close the Apple site has been triggered by the recent loss of two major contracts and difficulty attracting new work without discounting prices.
Printing of The Guardian's weekend supplement The Guide is moving to Polestar as part of a larger contract arrangement, and Irish broadcaster RTÉ has decided to relocate the printing of its weekly television listings magazine, RTÉ Guide, to Ireland.
Roy Kingston, Wyndeham Group's chief operating officer, said: "The loss of these titles has created substantial capacity at the company. Despite a considerable and concerted sales and marketing effort, we have been unable to secure sufficient replacement work within the timeframe, meaning that the business will start to generate unsustainable losses."
Wyndeham Group's chief executive office Paul Utting added: "We are not prepared to reduce prices to levels which make our business unprofitable. We cannot reduce prices to retain or win turnover at a time when the industry is facing unprecedented increases in its input costs."
He added the company has considered alternative plans including downsizing the site, but said that with "a substantially reduced turnover level", it could not make the necessary return.
If Wyndeham Apple closes, the intention is to move the magazine portfolio of its largest client, Trader Media Group, publisher of Auto Trader, to other web offset facilities within the Wyndeham Group.
The former Apple Web Offset site operates three 64pp Uniset presses, an 8pp mini-web used mainly for cover printing, four stitching lines and two perfect binders across three sites in Warrington.
If the closure goes ahead the presses would be decommissioned, although options for the bindery equipment remain under review.
The move follows last month's proposed closure of Wyndeham's Plymouth site and marks the ongoing consolidation of Wyndeham Press Group's expanded footprint in the wake of its acquisition of St Ives Web.