Banks and building societies are able to use the scheme to boost their borrowing but other lenders, such as Precise Mortgages, are unable to take part.
The FLS is aimed at both residential and business borrowers and Tucker, speaking personally, said that he felt money from the Funding for Lending Scheme was failing to reach businesses.
“Small and medium sized businesses are the lifeblood of the productive side of the economy,” he told the Treasury Committee.
“I am worried, as our others, that our current battery of credit policies might not be reaching as far into the SME sector as they might.”
He added that a solution to that issue could be extending the scheme to non-banks in the future.
“Not all lending to small firms in the economy comes from banks, it also comes from non-banks.
“I think we should have a think about can we harness non-bank lenders in some way, possibly via the banks.”
Fellow deputy governor Charles Bean, also speaking to the committee, added that he was happy with what the scheme had achieved and rejected calls to alter its parameters.
“It is not a scheme which lends itself to continuous tweaking in the same way in the same way you might with the base rate or quantitative asset purchases. What the FLS does is supply banks with funding cheaper than they could get in the market.
“We also put in extra incentives to encourage banks to lend more than they otherwise would have done. As far as banks are concerned they want some certainty with regards to the pricing of the scheme, and it wouldn’t be constructive of us to be tweaking the parameters month to month.
“If it was the case that we’d got the calibration of the scheme wrong we would see if we needed to change something. But frankly the way it is working at the moment is pretty much as we expected it to.
“We have seen the effect on funding costs we wanted to see, it has largely passed through to rates being charged, particularly on household residential mortgages.”
Tucker later raised the prospect of the Bank of England following Denmark in temporarily introducing negative interest rates to further boost lending and support the economy.
“This would be an extraordinary thing to do and it needs to be thought through carefully,” he said. “I hope we will think about whether there are constraints to setting negative interest rates.”