The president of the European Council has opposed Greece's demand for an emergency leaders' summit on the country's troubled bailout programme.
Donald Tusk argued that finance officials need to resume talks and agree within days on reforms needed.
Greek prime minister Alexis Tsipras spoke with Mr Tusk on Wednesday to propose the meeting of leaders from the 19 European countries that use the euro currency.
However, Mr Tusk sounded sceptical, arguing the finance ministers should make more progress before the leaders intervene.
Greece and its creditors - its European partners and the International Monetary Fund - have been struggling to agree on the reforms and cutbacks the country must make under the first review of its ongoing bailout programme, which was originally scheduled for last October.
Mr Tsipras' left-led government had hoped that a successful conclusion of the negotiations would allow the convocation of a meeting of eurozone finance ministers on Thursday to approve the agreement.
But now it looks as if the impasse could severely delay the deal that Greece needs before it can start official talks with creditors on relieving its crippling debt load.
An agreement would also release a long-delayed rescue loan instalment, without which Greece will be unable to make scheduled payments to its creditors in the summer.
Athens is already facing a liquidity crunch, and in February Finance Minister Euclid Tsakalotos warned that if the review stretches on into May or June, Greece is "done for".
Julius Baer bank analyst Eirini Tsekeridou said she expects the talks to continue until the main scheduled payment is due.
"Until an agreement is reached and the first review is completed there will be no further disbursements towards Greece," she said.
"Despite the statements about progress, we still believe the negotiations will drag until July, when Greece has to make a €2.2bn payment to the European Central Bank."
In Brussels, Mr Tusk said he would consult with the top officials from the eurozone and the European Commission but added that the eurozone finance chiefs - known as the eurogroup - need to set another meeting date by which they should agree on a deal.
"I am talking not about weeks but about days," he told reporters.
Mr Tsipras' office said the prime minister would talk with Mr Tusk again on Thursday morning.
EU foreign policy chief Federica Mogherini voiced confidence a deal can be reached "in a very limited time".
She said: "We believe all conditions are there to find a solution at the eurogroup meeting very soon."
Greece's finance ministry said there is agreement on creditor-demanded austerity measures worth 3% of GDP - or €5.4bn - by 2018. These will be achieved largely through pension and tax reforms.
However, disagreements remain over how to guarantee that an extra €3.6bn in savings that could be needed in the future will be implemented if deemed necessary.
Labour Minister George Katrougalos said: "I think the situation is serious. I'm not underestimating it.
"But I'm not afraid because I know - I want to believe - that Europe is still a political union based on agreements and efforts to achieve consensus."