Amid evidence that the Funding for Lending (FLS) programme has so far failed to get banks lending more, minutes of the Bank's most recent rate-setting meeting showed policymakers "saw merits" in boosting the scheme.
The Bank of England has offered more signs that a multibillion-pound scheme aimed at boosting credit to households and businesses will be ramped up.
Chancellor George Osborne said at last month's Budget that the Treasury and Bank were considering possible extensions to the FLS.
It is thought they want to split the scheme into two, as banks that are currently shrinking their legacy mortgage books are not able to qualify for the cheapest rates, which is holding back improvements in business lending.
The FLS is also likely to be extended past the current deadline of January 31 next year. The scheme was launched last summer by the Bank and the Treasury to offer lenders funding at low interest rates on condition it is passed on to households and businesses.
There were further signs in the Bank's minutes that policymakers believe FLS could be a more effective stimulus tool than its current quantitative easing (QE) programme, which was again held at £375 billion in April.
Minutes of the April monetary policy committee meeting showed that governor Sir Mervyn King and fellow policymakers David Miles and Paul Fisher failed to win further support for boosting QE by £25 billion. With inflation expected to rise above 3% in coming months, they were outvoted over fears that further easing might exacerbate this movement and prompt renewed weakness in sterling.
Inflation was stuck at 2.8% in March, official figures showed on Tuesday, and has been stubbornly above the Bank's 2% target since December 2009. Mr Osborne gave the Bank a looser remit on inflation last month, giving it scope to make "short-term trade-offs" between higher prices and growth, in an attempt to spur faster economic recovery.
But with fears about rising gas, electricity, water and food bills triggering a summer rise in inflation, the majority of MPC members opted to keep its QE programme steady for another month.
Economists are split on whether the Bank will opt for more asset purchases next month, or wait until the arrival of new governor Mark Carney in July. Much will hinge on whether the UK economy managed to grow in the first three months of the year - thus avoiding a damaging triple-dip recession.