It is believed UBS and Goldman Sachs are also among the financial institutions vying for work on the sale of part of the state-owned postal operator, which could see foreign investors buying a stake of up to 33% in Royal Mail.
NM Rothschild will separately advise Royal Mail, according to a report in The Times.
Rival postal operator TNT, which is part of the privatised former Dutch postal service TPG, became the front-runner this week for a new "strategic partnership" with the Royal Mail after Lord Mandelson, head of the Department for Business, Enterprise and Regulatory Reform, welcomed the company's expression of interest.
It is believed that Government ministers launched the search for private investment in Royal Mail when it became clear that the independent Hooper report on the future of the universal postal service would recommend the involvement of the private sector.
The proposed sale has outraged the Communication Workers Union, which is threatening to strike in protest at any move towards privatisation.
It emerged yesterday that private equity house CVC might also be interested in bidding for a stake. The company declined to comment.
A spokeswoman for the Communications Workers Union was angered by the news. She told The Times: "The prospect of a venture capital group buying part of the British postal service demonstrates the danger of any sell-off."