Outlaw confirmed that he and two other directors had received letters informing them their positions were at risk.
Paul Utting, chief executive of Wyndeham Press Group, said: "I can confirm that we are in consultation with a number of individuals as part of our ongoing management reorganisation.
"We are trying to make all of our publishing-facing sites in the south of England work together as one business and we want a single management team running those sites."
Utting added that it was a "completely logical" move to unify the management of sheetfed site Wyndeham Grange, in West Sussex, and web offset sites Wyndeham Heron in Essex and Wyndeham Impact in Hampshire.
The proposed redundancies at Wyndeham Heron follow the announcement that Wyndeham Grange has entered into consultation with 32 of its 96 staff, including finance director Andrew Emmings.
Wyndeham seeks to cut three Heron directors
Wyndeham Press Group has begun a 30-day consultation with three senior staff at its flagship web offset site, Wyndeham Heron, including sales and customer services director Alan Outlaw.
