Germany's Bild newspaper said on Thursday that the German government is opposed to a third bailout and would be ready for an extension of the current programme.

According to diplomatic sources, this extension would see the European Stability Mechanism (ESM), the eurozone emergency mechanism, lend Greece money in order to repay bonds to the European Central Bank.

The ECB owns €27 billion of Greek debt.

An ESM loan would relieve Greece of the over €6 billion repayment due to the ECB this summer.

Without a lifeline to help Greece repay the ECB, a source told EUobserver, the country would run out of liquidity at the end of September.

Another financing solution - going with an eventual extension of the bailout - would be to unblock €10.9 billion of funds normally reserved for the recapitalisation of Greek banks.

A diplomatic source told this website experts at technical level will now have to assess the impact of these options.

"Everyone wants to find a solution," another diplomatic source said.

"When there is a will, there is a way," Merkel said on the doorstep, adding that "the goal is to keep Greece in the euro area."

It was unclear however whether the institutions involved in the bailout negotiations - the EU, the ECB and the International monetary fund (IMF) - would be ready to back such a solution.

An extension of the bailout as well as an ESM loan to Greece would also need to be approved by some national parliaments.

"We had a very friendly meeting and we decided to intensify discussions in order to solve remaining differences and move towards a solution which guarantees a return to a socially inclusive growth," Tsipras told reporters after the meeting.

The Greek PM said that "the leadership of the EU understands that we need a viable solution (…) with a sustainable debt".

The two-hour meeting, which ended after midnight, was held on the margins of the EU-Latin America summit in Brussels.

It was the fourth trilateral meeting between the Greek, German and French leaders since March. This time they came with advisers, which suggest talks were more detailed than at previous meetings.

The Greek government has so far resisted creditors' demands to cut pensions and raise VAT, especially on energy.

More progress could be made on Thursday, when Tsipras is to meet the president of the EU Commission Jean-Claude Juncker.