Eurotunnel chief executive Jacques Gounon has met with bondholders to win support for a major restructuring plan.
Jacques Gounon wants to hammer out a consensus of opinion
The company wants to reduce its crippling debt levels, and while it has the backing of a group of banks, it is facing opposition from other investors.
Eurotunnel said almost all bondholders attended, and Friday's talks were a "big step" in reaching an agreement.
The company said it had put forward new proposals and planned another meeting with on Tuesday 11 July.
Eurotunnel had been excluded from renegotiating its debt problems, but managed to get a waiver period that allowed talks to continue until 12 July.
The company said that during its meeting on Friday it put "new ideas to creditors, present or represented, designed for their category of debt and compatible with the preliminary financial restructuring plan".
A key issue under discussion has been the amount of cash the bondholders wanted to be paid in order to allow the restructuring to go ahead. Many had complained that Eurotunnel was offering too little money.
According to the Channel Tunnel operator, a number of investors now want to retain some equity in the company.
A spokesman for Eurotunnel said that the terms of the restructuring deal allowed for their needs to be met, and it was now a question of getting all the sides to agree and rubber-stamp the terms of the agreement.
Eurotunnel faces financial collapse it is does not sort out its debts
"The hardest thing has been getting them all in the same room together," the spokesman explained.
"Slowly but surely, things are firming up."
The crisis at Eurotunnel has its origins in the construction of the channel tunnel, completed in 1994.
The tunnel cost about 14bn euros ($17.7bn; £9.8bn) to build, but traffic has never been nearly as heavy as was originally forecast, hurting Eurotunnel's revenues.
The firm has warned that it could go bankrupt next year unless it reaches agreement on a comprehensive financial restructuring.
It has reached a preliminary agreement with a group of banks, which would see its 9bn euro debt cut in half, though shareholders would see their holdings diluted.
Creditors holding the bulk of the firm's debt have approved the deal in principle.
But Arco, a group claiming to represent bondholders carrying about a third of its debt, opposes the plan, saying it offers poor value.
It is putting forward its own solution, which it says would lead to lower debt repayments and a better deal for both shareholders and creditors.
Arco was reported as not attending the meeting. Eurotunnel's spokesman said an Arco representative was present.
Analysts say that if a solution is not found, it is likely to be a matter of months before Eurotunnel hits the buffers.
Last year, rebel shareholders dismissed the company's board for failing to bring its financial problems under control.
Should the restructuring plan get the backing of bondholders next week, then shareholders will get their opportunity to vote on the deal on 27 July.