The European Central Bank has reportedly agreed to raise the emergency funding available to Greek banks to €68.3bn (£50.3bn).
The €3.3bn increase in the so-called Emergency Liquidity Assistance (ELA) is critical for Greece's banks.
Depositors have been taking savings out of the country, depleting the banks' access to cash to lend.
However, the Greek central bank is said to have requested an additional €10bn of emergency funding.
The ECB had already raised the amount available to Greek banks by €5bn to about €65bn last week.
The deal will give Athens breathing space to negotiate a loan deal with its European creditors.
Greece is asking the eurozone for a six-month extension of its European loan, a Greek government official said on Wednesday. It would not be a renewal of the current bailout agreement, which includes strict austerity measures.
On Monday night, Greece rejected a plan to extend its €240bn (£178bn) bailout, describing it as "absurd".
Greece is likely to run out of money if a deal is not reached before the end of February.
"We should extend the credit programme by a few months to have enough stability so that we can negotiate a new agreement between Greece and Europe," Greek Finance Minister Yanis Varoufakis told Germany's ZDF.
Government spokesman Gabriel Sakellaridis confirmed that meant Mr Varoufakis would be asking for a six-month extension to Greece's current loan.
Mr Sakellaridis told Greece's Antenna TV: "Let's wait today for the request for an extension of the loan contract to be submitted by finance minister Varoufakis.
"All along deliberations are going on to find common ground, we want to believe that we are on a good path. We are coming to the table to find a solution."
'Yes or no'
But he added the Greek government would not back down on issues that it considered non-negotiable.
German Finance Minister Wolfgang Schaeuble dismissed the Greek proposal, telling broadcaster ZDF on Tuesday evening: "It's not about extending a credit programme but about whether this bailout programme will be fulfilled, yes or no."
Mr Schaeuble added: "I don't have any new information, but there is no loan agreement, it's an assistance programme. And in this seemingly unimportant detail lies the key: Greece would like to receive credit, but not fulfil the conditions to allow Greece to recover economically."
In a surprise move, Greek MPs voted to elect pro-European conservative Prokopis Pavlopoulos as the country's new president on Wednesday.
The former minister and public law academic was put forward for the post in a bid to win much-needed cross-party support as Greece seeks to strike a deal with its international creditors.
Pavlopoulos was backed by the left-wing government as well as the main opposition party.
Conservative European Commissioner Dimitris Avramopoulos had been considered the front-runner for the largely ceremonial post.
An impasse over the selection of a new president triggered an early election last month that swept Syriza into government.
The Greek stock exchange rose 3% on Wednesday in morning trading in Athens as news of the loan extension application emerged, but later closed up just 1.1%.
The eurozone has given Greece until Friday to decide if it wants to continue with the current bailout deal.
Greece wants to replace the bailout with a new loan that it says would give it time to find a permanent solution to the debt crisis.
On Tuesday, Greek Prime Minister Alexis Tsipras called for a vote in the Greek parliament on whether to scrap the austerity programme on Friday, the same day as the eurozone deadline.
"We will not succumb to psychological blackmail," Mr Tsipras told parliament. "We are not in a hurry and we will not compromise."
US investment bank JP Morgan claimed over the weekend that €2bn worth of deposits was flowing out of Greek banks each week. It estimated that if that were to remain the case, they would run out of cash to use as collateral against new loans within 14 weeks.
JP Morgan's estimate is based on a calculation that a maximum of €108bn of deposits is left in Greek banks.
The most up-to-date figures from the Greek central bank show deposits dropped 2.4% month-on-month in December to €160.3bn from €164.3bn, marking the third consecutive monthly fall.
Dutch Finance Minister Jeroen Dijsselbloem, who is also chairing the Eurogroup meetings of eurozone finance ministers, warned on Monday night there were just days left for talks.
Mr Dijsselbloem said it was now "up to Greece" to decide if it wanted more funding or not.
Analysis: Theo Leggett, BBC business reporter:
The apparent deadlock in Brussels is hardly surprising, because the two sides have very different goals.
The Greek government wants to scrap the current bailout deal, because of the very painful programme of spending cuts and other austerity measures that come with it. Instead, it wants a bridging loan to help it meet its short term needs, while a new deal is hammered out. Having been elected on an anti-austerity ticket, it can't afford to back down, or it will be accused of betraying Greek voters.
But other members of the eurozone, and Germany in particular, have a very different agenda. They want Greece to accept an extension to the current deal - with the rather uncertain promise of "flexibility" if it plays ball.
They don't want to show any signs of weakness, because of the signal that could send to anti-austerity movements in countries such as Spain, Portugal or Cyprus.
It would also be politically toxic in Germany, where many voters dislike the idea that they are paying for Greece's mistakes.
That doesn't mean a compromise is impossible. It simply means any deal would have to be presented as both an end to the current austerity programme and a continuation of it. A political fudge, in other words - and Brussels has plenty of experience in putting those together. So a short-term solution is possible, but far from certain.
Key dates for Greece - and the eurozone
28 February - Current programme of loans ends
First quarter of 2015 - Greece's funding needs estimated at €4.3bn by end of March
19-20 March - EU leaders' summit
20 July - €3.5bn bonds held by the European Central Bank mature
20 August - €3.2bn bonds held by the European Central Bank mature
Greece has proposed a new bailout programme that involves a bridging loan to keep the country going for six months and help it repay €7bn (£5.2bn) of maturing bonds.
The second part of the plan would see the county's debt refinanced. Part of this might be through "GDP bonds" - bonds carrying an interest rate linked to economic growth.
Greece also wants to see a reduction in the primary surplus target - the surplus the government must generate (excluding interest payments on debt) - from 3% to 1.49% of GDP.
In Greece last week, two opinion polls indicated that 79% of Greeks supported the government's policies, and 74% believed its negotiating strategy would succeed.