The vote results that will be announced later in the day follow months of rolling, regional strikes over pay and job security which have already caused a backlog of letters and parcels.
Billy Hayes, general secretary of the Communication Workers Union, said he was confident that workers would authorize a strike.
"We don't have to take strike action, but it seems to have come to this because the government and Royal Mail have refused to engage the work force in modernization of the company," Hayes said in an interview with BBC radio.
Business Secretary Peter Mandelson has refused to intervene, but the union says the government, which owns Royal Mail Group PLC, has a responsibility to act.
The union and the Royal Mail blamed each other for the dispute amid claims that postmen and women were being put under "unbearable pressure" to implement changes.
Royal Mail's managing director Mark Higson said changes were being made in response to falling volumes of mail. Letter volumes were falling by 10 percent a year as people switched to other forms of communication such as e-mail and texting, Higson said, and Royal Mail faces competition from other carriers for parcel delivery.
Royal Mail plans no more changes affecting workers this year though more changes are planned next year, operations director Paul Tolhurst said.
"Change is a very difficult thing. Asking people to work an extra street is not easy. But we have to make sure our people work efficiently so we can deliver the best possible postal service," Tolhurst said.
As the strike threat loomed, one of Royal Mail's biggest customers, online retailer Amazon, said it was examining options.
"We have not canceled any long term contracts with Royal Mail," the company said in a statement. "They continue to be one of a number of carriers that we use."
However, Amazon said it was working on contingency measures with other carriers.