The president of Cyprus will later present political leaders with a “Plan B” for funding the controversial bailout, state TV has reported.
Cyprus’s banks, which have been shut all week to prevent mass withdrawals, are to stay closed until next Tuesday.
Politicians have been scrambling to find a way forward after a bank levy was rejected by parliament on Tuesday.
The levy was a condition of a 10bn-euro (£8.5bn; $13bn) EU-IMF bailout for Cyprus.
“A decision on a Cyprus rescue must be made on Thursday at the latest,” President Nicos Anastasiades was quoted as saying by the official CNA news agency.
Mr Anastasiades will put a proposal to a meeting of political party leaders meeting at 09:30 (07:30 GMT). It is then expected to go before parliament in the afternoon, according to CNA.
State TV said the plan might include a levy on bank deposits over 100,000 euros.
The previous proposals had also included a levy on deposits between 20,000 and 100,000 euros, which had outraged many Cypriots.
The new plan is also reported to involve nationalising pension funds.
‘Good beginning’
One official told the Associated Press that the new package would include “some form” of Russian help, but did not elaborate.
The Cypriot Finance Minister Michalis Sarris is in Moscow to negotiate assistance from Russia, which holds multi-billion dollar investments in Cyprus.
Mr Sarris said after talks with Russian Finance Minister Anton Siluanov that there had been “no offers, nothing concrete,” but “a good beginning”.
Talks are expected to continue in Moscow on Thursday.
Cyprus has attracted money through its low tax rates, with Russians holding between a third and a half of all Cypriot deposits.
Russian private and corporate assets in Cypriot banks are believed to total about 23bn euro, including many larger deposits, and Russian officials had expressed anger at the bank levy plans.
Analysts say Russia may provide more funding in return for interests in Cyprus’ offshore energy fields.
Bankruptcy fears
Monday 25 March is a scheduled bank holiday in Cyprus, and Thursday and Friday have now also been declared bank holidays. The stock exchange also remains closed.
German Finance Minister Wolfgang Schaeuble has warned Cyprus that its banks might never be able to reopen if it rejected the bailout.
Bank mergers, a bond issue, and more Russian funding have all been mentioned as ways to help the country out of the crisis.
One offer of help has come from Cyprus’s Orthodox Church, which is a major shareholder in the third-largest domestic lender, the Hellenic Bank.
Archbishop Chrysostomos I said on Wednesday the Church was willing to mortgage its assets to invest in government bonds.
The establishment of a “bad bank” which would take on risky assets held by Cypriot banks has also been mentioned by officials.
The BBC’s Mark Lowen, in Nicosia, says Cyprus is a resilient nation and the banks are still giving out cash through machines – although with limits, and some are running low.
Some businesses are now refusing credit card payments, our correspondent reports.
On Wednesday, German Chancellor Angela Merkel said she regretted but respected the Cypriot vote.
She said the eurozone had a duty to find a solution for Cyprus, but added that the country’s current banking system was “not sustainable”.
Cyprus’ banks were left exposed following the debt crisis in Greece and there are fears Cyprus could go bankrupt if they fail.
The controversial levy had been proposed as the condition for the 10bn-euro bailout. Cyprus was expected to raise 5.8bn euros through the one-off tax on bank savings.
The plan was altered on Tuesday to exempt savers with less than 20,000 euros, but a 6.75% charge on deposits of 20,000-100,000 euros and a 9.9% charge for those above 100,000 euros remained.
However, parliament rejected the deal, with 36 MPs voting against it, 19 abstaining and none in favour.