A licence extension would significantly improve the troubled Anglo-French company's long-term finances and would help to secure agreement with its bankers over a reconstruction of its tattered balance sheet.
Eurotunnel has been lobbying to have the licence extended to 99 years and is thought to have won the backing of the French government.
Eurotunnel is a more sensitive issue in France than Britain: 640,000 of the 780,000 shareholders are French. Last week, angry French shareholders held a demonstration at Eurotunnel's terminal in Calais. Since 1989, they have seen their shares lose more than 90 per cent of their value.
However, an extension to 99 years would deprive British and French taxpayers of 34 years of revenues from the tunnel, which is presently due to be handed back to the British and French governments in the year 2052.
Neither government is allowed to finance the tunnel project directly, according to the terms of the 1983 treaty that laid the foundations for the initiative. However, a precedent for lengthening Eurotunnel's ownership of the tunnel was set in 1993, when the two governments agreed to extend the licence from 55 years to 65 years.
With Britain desperate for allies in its battle to have the beef export ban lifted in Europe, Mr Major might look favourably on licence extension in return for support from Mr Chirac.
Patrick Ponsolle, the French co-chairman of Eurotunnel, is said to be incensed that London & Continental Railways, the consortium awarded the contract to build and operate the high-speed rail line that will link the tunnel with London, was given a 999-year concession. He believes Eurotunnel, deserves longer than 65 years.
One source close to Eurotunnel said: "An extension would help with the reconstruction." It would give the company longer to repay its debts and would enable it to bring forward the date at which it starts paying dividends.
"If a fairy godmother in the shape of Mr Chirac and Mr Major came along and gave the company an extra 34 years to repay its debts, the whole thing would be much more attractive."
Eurotunnel last week began formal talks with the six steering group banks, which represent the interests of 225 banks owed a total of pounds 8.4bn. Both sides are proceeding on the assumption that there is no extension to the licence, but sources say any extension would greatly help negotiations.
Eurotunnel is pressing for a dramatic cut in the interest rates it pays, from 9.5 per cent or more to just 7 per cent. This is the rate paid by low-risk utility companies, which it argues it will start to resemble when the reconstruction is complete.
The restructuring would involve the banks swapping some of their debts for a 49 per cent equity stake in Eurotunnel, according to leaked details of the initial proposals.
Eurotunnel hopes to be able to report some progress on the talks by the annual shareholders' meeting in late June. Sir Alastair Morton, the British co-chairman, plans to retire once the restructuring is complete, possibly this autumn, resisting pressure from some bankers to go earlier.Reuse content