The court appointed Mr Badinter and Lord Wakeham in February to handle the refinancing negotiations with Eurotunnel's creditor banks following a request by the company.
The mandates of the two mediators, which expire 30 June, could be extended,"if there are reasonable chances of seeing a solution," Mr Mattei said.
He added that the last meeting between the two parties and the mediators took place recently. The mediators would hand in a report before end month.
Mr Mattei warned that there could be serious legal complications if Eurotunnel was found to be legally incapable of paying its debts, which would trigger clauses in its contracts under which new managers could be substituted to take control of the tunnel.
Eurotunnel would have no business left once the new operator took over. This substitution clause is a fundamental part of the Anglo-French agreement on the operation of the tunnel.
He said that if mediation failed and the substitution clause was invoked, the tribunal would open a procedure of legal reappraisal.
He added: "I am not sure if the substitution clause could be applied as easily as certain parties think and that its consequences will be as light as some seem to believe."
Eurotunnel suspended interest payments on most of its pounds 8bn debt in September. "Given that this affair is based on a hybrid legal basis - civil and corporate laws, within a Franco-British covenant ... this affair is a judicial monster," he said.
"The mediators have tried to impress on the banks' representatives that there have to be other solutions than invoking the substitution clause."
The interests of Eurotunnel's shareholders were "one of his concerns," Mr Mattei said.