Sky's City editor Mark Kleinman says that Kuwait and Singapore-based wealth funds are among those which have share orders worth "hundreds of millions of pounds".
His sources suggest that the two top funds are expected to receive shares "because of ministers' desire to see Royal Mail have a geographically-diverse investor base".
Yet many UK investors are likely to be left out. The sale of Royal Mail shares has been hugely oversubscribed with more than 700,000 investors applying. Just a fifth have been set aside for individuals, with another 40 per cent reserved for City institutions.
Business secretary Vince cable has said that he wants the order book to be "dominated by responsible long-term institutional investors".