Their junior colleagues at the GRA yesterday rejected a similar proposal – which will see them walk off the job for four Fridays this month.
The Cabinet is meeting this afternoon to discuss the matter.
AGSI President Antoinette Cunningham wouldn't be drawn on what the Department of Justice is offering middle ranking Gardaí as she made her way into the meeting.
The Garda Representative Association which represents rank and file Gardaí who make up the vast bulk of the force – rejected their pay offer yesterday – signalling their industrial action is likely to go ahead on Friday.
It's believed the Labour Court may step in but back up plans to keep the public safe during a strike are becoming more important.