Chicago Fed President and FOMC voter Goolsbee warned that there are signs that investors in the U.S. bond market are starting to anticipate higher inflation, which would be a "major danger signal" that could disrupt rate setters' plans for rate cuts.

In the week before Goolsbee made the above remarks, a closely watched University of Michigan survey showed that long-term inflation expectations for U.S. households reached their highest level since 1993. Goolsbee said: "If you see market-based long-term inflation expectations changing as they have in the past two months, I would consider this a major danger signal that needs to be highly monitored." The five-year forward rate is currently at 2.2%, while the University of Michigan survey shows that consumers expect long-term inflation to be at 3.9%.

Goolsbee said that if investors' expectations start to converge with those of U.S. households, the Fed will have to take action: "You almost have to deal with this issue in any scenario." he said.