This week's FOMC statement was a unanimous decision.
Williams recognized that "the big story for the Fed right now is inflation," and that with a strong dollar and low energy costs "we're going to see inflation run well below 2 percent for the next several months and a couple quarters."
He said that once the effect of these factors run through the economy, inflation should begin picking up in the second half of 2015.
Read MoreFed's Williams: 'Turbulence' likely if this occurs
By the end of 2016, he said, the U.S. should be close to the Fed's 2 percent inflation target.
Given this projection, Williams said he thought "around the middle of this year is the time that I think, in my view, that we'll be getting closer to 'Should we raise rates now, or should we wait a little longer, collect some more data, get more confidence in the forecast?'"
"Around midyear is a good guess for when we really are getting close to that point that raising rates will be appropriate," he said.
Read MoreFed: Will remain 'patient,' upgrades economy
In other words, Williams predicted that the Fed would begin discussions of a rate increase despite neither wage growth nor inflation hitting the central bank's targets.
He explained that the projections of nearly full employment and the economy's "extraordinary monetary accommodation" (zero-interest rates, and a more-than-$4 trillion balance sheet) would justify these discussions.
Williams had predicted earlier this month that "turbulence" would be likely if Fed tightening occurred while the European Central Bank and the Bank of Japan increased stimulus. The ECB went on to announce an open-ended bond-buying program last week.