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"That would be pretty aggressive," she said. "There must be some outspoken people who are pretty concerned that they need to move even faster."

St. Louis Fed President James Bullard is one such member, telling CNBC on Tuesday that he thinks tapering should be more aggressive in case the Fed needs to rate interest rates next year to combat persistent inflation.

At the September policymaking session, the committee voted unanimously to hold the central bank's benchmark short-term borrowing rate at zero to 0.25%.

The committee also released the summary of its economic expectations, including projections for GDP growth, inflation and unemployment. Members scaled back their GDP estimates for this year but upped their outlook for inflation, and indicated they expect unemployment to be lower than earlier estimates.

In the "dot plot" of individual members' expectations for interest rates, the committee indicated it could begin raising interest rates as soon as 2022. Markets currently are pricing in the first rate hike for next September, according to the CME FedWatch tool. Following the release of the minutes, traders increased the likelihood of a September hike to 65% from 62%.

Officials, though, stressed that a tapering decision should not be seen as implying pending interest rate hikes.

However, some members at the meeting showed concern that current inflation pressures might last longer than they had anticipated. Traders are pricing in a 46% chance of two rate hikes in 2022.

"Most participants saw inflation risks as weighted to the upside because of concerns that supply disruptions and labor shortages might last longer and might have larger or more persistent effects on prices and wages than they currently assumed," the minutes stated.

The document noted that "a few participants" said there could be some "downside risks" for inflation as long-standing factors that have kept prices in check come back into play. The majority of Fed officials have been holding to theme that the current price increases are transitory and due to supply chain bottlenecks, and other factors likely to subside.

Inflation pressures have continued, though, with a reading Wednesday showing that consumer prices are up 5.4% over the past year, the fastest pace in decades.