Any action by members of the Communication Workers Union will affect mail processing, distribution and delivery services in areas including Edinburgh, Dunfermline and Falkirk.
The union said Royal Mail had refused to obey a court order to rescind its dismissal of postman David Mitchell in December 2014.
His colleagues at Cupar delivery office in Fife have already taken industrial action, while thousands of local residents have signed a petition demanding his reinstatement.
Mr Mitchell was dismissed after 27 years of service over allegations of theft, which he denies.
A Royal Mail spokesman said: “Royal Mail is still hopeful of finding a resolution.
“We will not reinstate Mr Mitchell, as we believe that the trust between employee and employer has broken down.
“As we feel unable to reinstate Mr Mitchell, the judge ordered Royal Mail to pay additional compensation, which Mr Mitchell has now received. The legal proceedings have now concluded.”