Shadow postal affairs minister Ian Murray said the aim was to halt the sell off before it starts.
Any vote in Parliament would be held in the next few weeks as the coalition prepares to offer shares to the public and institutional investors.
Mr Murray told a fringe meeting at the Labour conference in Brighton that the party was "fundamentally against" privatisation, warning it would hit services and threaten post office closures.
"We think we can have one last vote when we get back from the recess. Let's push for a vote in Parliament and stop the privatisation before it starts, for the benefit of the postal service and its workers."
Leaders of the Communication Workers Union, Unite and the Federation of SubPostmasters (FSP) told the meeting prices would increase, the six-days-a-week universal service would be under threat and deliveries would worsen under privatisation.
Dave Ward, deputy leader of the CWU, said he expected Labour to stand "shoulder to shoulder" with unions in fighting the sell-off.
"This is a crunch moment, and the party cannot say it is opposed to privatisation and not follow it up with a commitment to renationalise."
The union is to ballot members for a national strike over pay, pensions, jobs and other issues linked to privatisation, with any action likely to start in mid-October.
Mr Ward said no member of the CWU had contacted him about the offer of free shares, with workers more interested in opting out.
"They know their pensions, jobs and working conditions are more important."
George Thompson, general secretary of the FSP, said the public needed to be told that thousands of post offices would be at risk if the sell-off goes ahead.
"If we make the public aware of the dangers to the six days a week delivery service we can still stop this privatisation."
Tony Burke of Unite said the public, MPs, the Countryside Alliance and postal workers and managers were all opposed to privatisation.
"Labour should pledge to renationalise a privatised Royal Mail. It would be a vote winner."