The paper, citing senior European Union diplomats, said the euro zone will endorse a five-fold increase in the 440-billion-euro bailout fund, giving it some two trillion euros to use to help troubled governments and banks withstand the impact in the event a troubled country defaults.
The paper said confidence that the plan would be approved at the summit was on the rise after Moody's warned it might put France's top AAA credit rating on review, citing the potential cost of bailing out troubled banks or other members of the euro zone.
U.S. stocks and the euro extended gains after the report while Treasury debt prices turned negative.
Brian Dolan, chief strategist at Forex.com in Bedminster, New Jersey, said the report, if true, "would be what the market's been looking for, and two trillion seems to be in the right neighborhood."
But he said an earlier warning from German Chancellor Angela Merkel that leaders would not solve the debt crisis in one summit meant he was taking the report "with a grain of salt."
"We've seen a lot of these European reports that something was imminent only to be disappointed the next morning," he said.
Markets have been on edge for fear European leaders would not agree on a comprehensive plan to address the crisis, which has already forced Greece, Ireland and Portugal to seek bailouts and has driven up borrowing costs in Italy and Spain.
European banks with heavy exposure to troubled sovereign debt have also found it harder to fund operations, sparking fear that governments may have to bail them out.
According to the Guardian report, France and Germany agreed that Europe's banks should be recapitalized to meet the 9 percent ratio the European Bank Authority is demanding after having examined the exposure levels of between 60 and 70 "systemic" banks.
While French and German banks are said capable of meeting the new capital ratio on their own, other countries' banks may need help from the state or the expanded bailout fund, known as the European Financial Stability Fund, the paper reported.
Berlin and Paris are also said to be closer to agreement on increasing private sector involvement in a second 109-billion-euro rescue package for Greece. The voluntary "haircut" for bond holders was set at 21 percent in July but worsening financial conditions have spurred Germany to push for private creditor losses of up to 50 percent.
(Reporting by Steven C. Johnson; Editing by James Dalgleish)