"We now expect that we will have a plan that can pass the House, pass the Senate and be signed by the president," Republican Senator Robert Bennett of Utah said after meetings with lawmakers on Thursday.
Details of the package were not immediately available but it is tipped to include restrictions on executives' pay as well as oversight requirements.
The benchmark Dow Jones index rose after Senator Dodd's comments, to close 198.09 points, or 1.83%, up at 11,023.26.
Presidential candidates Barack Obama and John McCain are in Washington for the talks.
The pair are due to hold a presidential campaign debate on Friday, but Mr McCain had said it should be called off because of the pressing financial crisis.
However, on Thursday evening Mr McCain's campaign team said the Republican senator had not yet decided whether to attend the debate.
George W Bush on the bail-out
The bail-out has been under scrutiny with politicians on both sides nervous about the deal being rushed through too quickly.
Of particular concern has been the issue of pay for the bosses of the firms in question, as well as concerns over the cost of the plan to the US taxpayer.
But both US Federal Reserve head Ben Bernanke and Mr Bush have warned that without a deal, it would cause a significant set-back to the economy as a whole.
British Prime Minister Gordon Brown, who is due to meet Mr Bush in Washington to talk about the financial turmoil on Friday, said he supported the US initiative to help bolster markets.
Those in favour of the deal have argued that it would:
Boost global financial stability
Increase investor confidence
Prevent a global slowdown
Encourage banks to lend to each other, and beat the credit crunch.
Those with reservations have said the bail-out would:
Cost the taxpayer too much money
Benefit bosses of firms who have taken huge risks
Increase state debt
Give too much power to the US Treasury.
One of the main uncertainties of the bail-out is what the true cost will be, and how the Treasury will price the bad debt that it is planning to acquire.
Under the preliminary plan, the government would acquire the bad, mortgage-backed assets of finance firms in a move to ensure they do not fold, to prevent further problems.
The fear is that if more finance firms go under this will have a knock-on effect on other sectors of the economy, further worsening the credit crisis.
Even as markets rose sharply, there are many ongoing questions about what a final plan would look like.
The BBC's business editor Robert Peston said the ongoing uncertainties could be "boiled down to one dilemma: if the bail-out is used to punish the banks it probably won't save the global financial system.
"But if the banks aren't punished, then US taxpayers may well feel that their pockets have been picked."
The package was proposed after a period in which markets saw almost unprecedented global turmoil and upheaval.
Key investment firm Lehman Brothers, the fourth largest investment bank in the US, filed for bankruptcy protection and the government had to intervene to rescue insurance giant AIG.
Meanwhile Bank of America stepped in to buy Merrill Lynch.
And investment banks Goldman Sachs and Morgan Stanley changed their status, enabling them to tap into commercial banking, effectively marking the end of an era on Wall Street.
The bail-out is being promoted as a way to help boost the outlook for banks, and improve the availability of credit which has been harder to obtain for banks and businesses as well as individuals.
But not everyone sees the bail-out as the right solution.
Senator Bernie Sanders organised a petition which attacked what it said was the Treasury's attempt to enable bosses to "continue to make exorbitant salaries and bonuses," reported Agence-France Presse.
"The wealthiest people, those ... in the best position to pay, are being asked for no sacrifice at all," read a petition to Treasury Secretary Henry Paulson.
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