The first meeting of the Fed since Donald Trump took office as president discussed the possibility of a rate rise as early as March.
Most economists have been forecasting a rise in June.
However, Fed officials appear divided on the timing of a rise amid uncertainty over Mr Trump's policies.
"Several'' expressed fears that unemployment could fall substantially below the Fed's 4.8% target. That could trigger inflation pressures and force the Fed to boost rates at a faster pace than financial markets expect.
Unemployment in December was 4.7%, although it was back at 4.8% in January.
Paul Ashworth, chief US economist at Capital Economics, said the "fairly soon"' phrase in the minutes "clearly leaves the door open to a March rate hike, although ... we still think the Fed will delay until June".
IHS Markit said the minutes and other recent comments signalled that a March rate hike was a "strong possibility".
If inflation and employment data for February were "in line with the recent trends", the Fed might "have no excuses to hold  off".
Ian Shepherdson, chief economist at Pantheon Macroeconomics, said the next increase was more likely to come in May than March unless there was a big increase in employment in February.
The minutes also showed that a couple of Fed officials had suggested the central bank might need to alter the wording of its policy statement.
The bank's assurances that it planned to raise rates at a "gradual" pace could be "misunderstood as a commitment of only one or two rate hikes per year", they argued.
The Fed left its key interest rate unchanged at the 31 January-1 February meeting.
In December it boosted its key rate by 0.25 percentage points to a new range of 0.5% to 0.75%.
The Fed had waited a full year to raise rates for a second time after its initial rate hike in December 2015.
Federal Reserve officials have said they may need to raise interest rates "fairly soon" if the economy stays strong, minutes of their meeting show.