The threatened post offices are on Manchester Road in Leigh, Leigh Road in Daisy Hill and Hart Common on Wigan Road in Westhoughton.
A six-week public consultation started yesterday on the future of 67 branches in the Post Office's Greater Manchester with High Peak region.
Leigh Coun Myra Whiteside, a former Post Office who successfully fought to keep one Leigh Post Office open during the last round of cuts, said: "It's so difficult because it's taking a resource away from the public.
"On the other hand I understand why they have to look at the future of some of the branches.
"We fought well to keep the Railway Road branch and we had to work hard that it didn't meet the criteria for closure."
All objections should be received by July 21 and people wishing to express their views can write to Richard Lynds, network development manager, c/o national consultation team, freepost consultation team. Alternatively, email consultation@postoffice.co.uk or call the customer helpline on 08457 223344.