International lenders estimate that Greece will need around €10-11 billion from the second half of 2014 to keep it going next year and in 2015.
But several eurozone governments are reluctant to extend any further loans because of negative public opinion, with voters tired of bailing out other countries after three years of the sovereign debt crisis.
"As far as the potential need for a third programme for Greece is concerned, it's clear that despite recent progress, Greece's troubles will not have been completely resolved by 2014," Jeroen Dijsselbloem told the European Parliament, during an exchange of views with the committee on economic and monetary affairs.
"It is realistic to assume that additional support will be needed beyond the programme. In this context, the Eurogroup has indicated clearly that it is committed to providing adequate support to Greece during the current programme and beyond until it has regained market access," he said.
Some form of debt relief for Athens on the cards
Dijsselbloem, who is also Dutch finance minister, said that separately, once verified Greek public finance data for 2013 is available in April 2014, the eurozone may consider some further form of debt relief for Athens.
"The Eurogroup agreed last year to consider additional measures if necessary, such as further reductions of the interest rates on Greek loan facilities... if Greece were to meet precise conditions," Dijsselbloem said.
"We will not be any position to assess whether these conditions have been fully met until April next year," he said.
Meanwhile, Dijsselbloem said that Ireland will get eurozone support to smoothly exit its bailout programme at the end of this year.
"Ireland's performed very well in its programme and will exit the programme, but there will be measures to support its gradual exit," he said.