National Express has not commented on the development
A major shareholder in National Express has joined with a private equity firm to formulate a possible takeover bid.
The Cosmen family from Spain, which owns 18.5% in the transport firm, has teamed up with CVC Capital Partners.
CVC confirmed the consortium had made an initial proposal "to acquire for cash" all shares in National Express.
It comes after First Group dropped out the running as a possible suitor, and after National Express said it had been approached by an unnamed suitor.
National Express - which operates bus and rail services - has not commented on any potential deal, which could be worth more than £500m ($800m) according to the Financial Times.
Shares in National Express were ahead by more than 9% at midday on the London Stock Exchange.
Four years ago the Cosmen family sold the coach firm Alsa to National Express for £149m and a 10% holding in the firm, which employs 43,000 people through operations in the UK, North America and Spain
The Cosmen stake has been built up since then and Jorge Cosmen is deputy chairman of the National Express board.
On Wednesday, First Group had said it would be "inappropriate" to consider a formal takeover of National Express, because of uncertainties surrounding the business.
The government is set to take the National Express-run East Coast main line into state ownership, after the firm asked for its contract to be renegotiated.
National Express has also been warned its other rail deals may be terminated.
When the government announced it would be taking the East Coast route into state ownership, Transport Secretary Lord Adonis said there might be grounds to end National Express's other two franchises - East Anglia and the London to Tilbury and Southend operation.
However, National Express has said it feels the government has "no grounds" to do this and will challenge any such attempt in court.