Greek prime minister Antonis Samaras has called for more time to carry out spending cuts and economic reforms, to help revive the economy.
He meets the head of the Eurozone finance ministers Jean-Claude Juncker on Wednesday and French and German leaders later in the week, the BBC is reporting.
At issue is whether Greece has done enough to receive its next 31.5 billion euro bailout payment.
Failure to unlock the funds could lead to Greece defaulting on its vast public debt and possibly leaving the eurozone.
Mr Samaras is under pressure to show Greece can fulfil its commitment of 11.5 billion euros in public spending cuts within two years in order to qualify for the money.
At the talks with Mr Juncker, he is expected to float the idea of Greece being given a two-year extension to the deadline.
His argument is expected to be that Greece has lost time because of general elections this year and that it is more realistic to adjust more gradually, easing the intense pain felt by the Greek people.
A government source has told the BBC that the prime minister will not press the issue, fearing it might cause bad blood with Greece's international lenders before they deliver their report in September on the country's progress.