Ahead of announcing the legislation on Thursday, Mandelson told The Guardian that he believes he could placate the Labour rebels with certain compromises.
Mandelson said: "I believe that we can put in place certain conditions, certain limitations, certain qualifications that will address the concerns of Labour MPs. I am prepared to accommodate their concerns during the passage of the bill."
His words follow a report at the weekend that the Danish and Swedish post offices, which are in the process of merging, are studying a joint bid for a stake in Royal Mail.
They join a list of potential buyers including the favourite to succeed, Dutch company TNT, and private equity firm CVC Partners.
Last week the Sunday Telegraph quoted a government source who said the Labour chief whip had told the prime minister the size of the parliamentary rebellion against the proposals meant he did not have the numbers to get the plans through parliament without relying on the support of the opposition or making compromises.