The efforts are being spearheaded by Eric Dinallo, the New York state insurance superintendent, who is being privately supported by the New York Federal Reserve Bank and other regulators, people familiar with the regulators said.
Perella Weinberg, an advisory firm based in New York, has been hired as a financial adviser by Mr Dinallo's department, according to people briefed on the plans. The company is led by Joseph Perella, a former Morgan Stanley mergers and acquisitions executive, and Peter Weinberg, who previously ran Goldman Sachs's European business. The executives were not immediately available for comment.
Mr Dinallo, who had said he is in contact with federal regulators, met about a dozen banks last week, asking them to provide $5bn to $15bn of funds for the bond insurance sector.
Under plans being discussed at the weekend, banks would provide back-up lines of credit to bond insurers such as Ambac and MBIA. While there was no indication any banks had agreed to such an idea, credit lines could help the insurers stave off credit rating downgrades.
Some bankers hope the discreet involvement of the Fed will give the initiative greater momentum, given its influence on Wall Street. In recent weeks, for example, the Fed has been discreetly urging big US banks to shore up their own capital base - with considerable success.
The rescue efforts come amid concerns that bond insurers are running out of time to reassure rating agencies that they have enough capital to deal with losses related to guarantees of bonds exposed to subprime mortgages.
Debt markets are pricing in the likelihood that bond insurers will lose their Triple-A status - in sharp contrast to the stock markets, which rallied sharply last week after news of a potential bailout emerged.
The loss of the Triple-A ratings could lead to losses for banks, some of which have large exposures to hedges and bonds whose value depends on the credit insurers maintaining the highest credit rating. Banks have already written off more than $100bn of exposures related to subprime mortgages.
One senior executive at a bond insurer said any rescue would be viewed positively by the rating agencies but that time was an important factor.
"The challenge is that the rating agencies have no firm deadline to complete their reviews, so it's hard to know how long they will be willing to wait," he said.
Standard & Poor's, the credit rating agency, told the FT it would probably take a "conservative" stance towards any bank bailout plans. Dick Smith, an analyst at S&P, said: "A bailout is currently not factored into the ratings."
MBIA and Ambac are working on finding fresh sources of capital. Ambac is under more immediate pressure because it ditched plans for $1bn of new equity. MBIA completed its $1bn capital raising and is also finalising a deal with Warburg Pincus, private equity investors, for a further $1bn. MBIA announces its results on Thursday.