Mr Tucker told MPs that charging commercial banks for the money they hold on reserve is a "pretty radical idea" to encourage them to lend but cautioned it is not "the answer to the universe".
At the moment banks receive the Base Rate of 0.5% on reserves.
But there is growing disquiet that measures such as providing banks with cheap financing through the Funding for Lending Scheme (FLS), is not feeding through in loans to small and medium-sized enterprises.
Denmark and Sweden have tried negative interest rates but many economists are sceptical that the policy has worked.
Samuel Tombs, economist at Capital Economics, said negative interest rates would see the amount paid to savers cut further. He added that banks could increase charges to borrowers in an attempt to recoup lost interest.
The chairman of the Treasury Committee, Andrew Tyrie, said: "The lack of lending to SMEs is inhibiting economic growth in the UK.
"The Monetary Policy Committee (MPC) is right to be looking at additional tools, or changes to existing tools, that could help.
"Some of the proposals we heard, such as moving to negative interest rates, are radical; others are not. They all warrant consideration."
Mr Tucker said he is open to adding to asset purchases under quantitative easing (QE) and said he wants to explore ways of improving companies' access to working capital.
Meanwhile, in a speech last night, Paul Fisher, the Bank's executive director for markets, insisted that FLS has been "remarkably successful" in cutting banks' funding costs.
The next stage of banks passing on lower funding costs to their customers "is happening", he said.
He added: "It is up to banks to deliver."
Mr Fisher and Bank Governor Sir Mervyn King were among those who unsuccessfully called for the £375 billion QE scheme to be extended.
Mr Fisher said a £25bn extension "could be the first instalment of a more prolonged run of purchases".