CVC, which owns a large stake in the Belgian postal service, is thought to have impressed the Government because it is proposing the injection of a significant sum of money into the modernisation of the company's technology and infrastructure.
TNT's proposal, the only firm alternative, is focused on securing control of GLS, Royal Mail's profitable parcels arm, along with more say over the board and strategic matters.
However both offers fall well short of the Government's expectations and may end plans for the controversial sell-off.
A number of other potential bidders, including Deutsche Post of Germany, considered submitting proposals but then decided against it.
The second reading of the bill for the part-privatisation of Royal Mail is expected to take place in the House of Commons on June 9, where it will face strong opposition from disgruntled MPs who argue the move would breach a Labour manifesto commitment.