The meeting in Berlin follows the broad deal reached in Malta over the weekend by Eurozone finance ministers to get Greece out of its £73.4billion bailout programme.
Germany has been clear this year it does not want to keep sending cash to Athens, and has said the IMF needs to be a full participant in the next phase of the Greek rescue – something Mrs Merkel and Christine Laguarde are set to address today.
Greece has agreed to implement additional austerity measures on condition of further debt relief which will enable the country to be included in the ECB's bond buying scheme, prime minister Alexis Tsipras said on Sunday.
Angela Merkel and Christine Lagarde met in Berlin to discuss Greece
Athens struck a deal with its international creditors at Friday's meeting on key elements of a reform package which could unlock bailout funds for the country to help it repay maturing debt in July.
Athens agreed to take measures that will cut government spending on pensions by 1.0 per cent of economic output in 2019, a year after its current €86billion bailout programme expires.
Christine Lagarde (L), and German Chancellor Angela Merkel (R) during a joint press conference
Greece agreed the basis of a bailout with the IMF on Friday
It also committed to tax reforms in 2020 to generate additional revenue equal to another 1 per cent of gross domestic product, mainly by lowering the current income tax exemption threshold.
To make the deal more palatable for Greece the lenders agreed that if budget savings targets are exceeded, Athens will be allowed to implement relief measures to boost the economy.
Get Quotes on Home Insurance
However, whether Berlin will be happy with this arrangement will be revealed following today's meeting.
Ahead of the meeting German finance minister Wolfgang Schaüble attempted to downplay the differences between Berlin and the IMF over Greek debt, saying it was natural "when we try to calculate how it will develop until 2070 to end up with different conclusions".
Protests have been taking place in Greece over austerity measures
Many Germans do not want to spend more money on Greece
He repeated the Greek bailout programme "can move forward only with the participation of the IMF, which is a part of it".
He said: "Otherwise, we and other member states will have to ask our parliaments to give us a mandate that will allow us to negotiate a programme with the IMF."
Mr Schaüble added that would be "completely absurd and could not work".