TNT's parent company, Dutch service TPG, is understood to be one of the companies interested in the share. The other is parcel courier DHL, part of Deutsche Post, The Daily Telegraph reported today.
The deal is estimated to be worth £3 billion and would see at least a third of the state-owned Royal Mail sold.
TNT has emerged as the key competitor to Royal Mail in the deregulated postal market, collecting more than a billion items of commercial mail in Britain every year, much of it transactional and direct mail.
Britain's postal service has been Government-run since it was set up in the 19th century. Labour said it would keep the service in public hands in the run up to the 2005 election. The Post Office and Royal Mail have been losing money and is facing a £7 billion pensions bill. Ministers therefore have been forced to act.
A spokesperson for Royal Mail said the company has not seen the Hooper Report yet, which outlines future plans, and therefore cannot comment on its content.