The minutes from October's MPC meeting show the nine members voted unanimously to maintain QE at £375 billion as "there was little to be gained" in changing the programme.
However, there were "differences of view" on prospects for economic growth and whether there was a need for more QE in the future.
The minutes said: "Some members felt that there was still considerable scope for asset purchases to provide further stimulus."
The MPC said projections on growth and inflation over the medium term had not changed much although a predicted pick up in growth was taking longer than expected to come through. It predicted that inflation is likely to stay close to its 2% target, although the meeting took place prior to recent price hikes by utility companies.
Many economists believe a further £50bn will be added to QE following November's MPC meeting.
Vicky Redwood, from Capital Economics, said: "Interestingly, the minutes suggest that the Committee is not too worried about the deterioration in the near-term inflation outlook – although the meeting took place before the latest announcements of utility price rises – and saw little change to the medium-term outlook for growth and inflation.
"Overall, then, it is a close call whether a majority votes for more QE next month.
"But the fact that at least some members are clearly convinced of the need to do more persuades us to stick with our forecast of a £50bn increase."
Bank of England chief economist Spencer Dale and external MPC member Ben Broadbent both opposed the last expansion of asset purchases in July and last week another external member, Martin Weale, also expressed scepticism about further purchases.
An interest rate cut, from 0.5% to 0.25%, is thought to be unlikely as the minutes did not report any discussion of the move.
Howard Archer, chief UK and European economist at IHS Global Insight, said: "We remain doubtful the Bank of England will trim interest rates from 0.50% to 0.25% given ongoing scepticism within the MPC that such a move would have a net overall beneficial impact.
"There is concern within the Bank of England that even lower interest rates would hit banks' profit margins and constrain their ability to lend. There is also concern that the functioning of money markets would become impaired."
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