Chicago Federal Reserve President Austan Goolsbee voiced concern Friday about the latest inflation readings, telling CNBC that the U.S. central bank will probably need to take action as price pressures move further away from its goal.

In an interview on 'Squawk Box,' Goolsbee said he believes the central bank 'has definitely got work to do to continue to reestablish its credibility' on inflation.

His remarks came shortly after the Bureau of Labor Statistics reported that the producer price index, a closely watched gauge of wholesale prices, rose 0.3% in October. The monthly increase was slightly smaller than economists expected, but it left wholesale prices up 6.5% from a year earlier, the largest annual gain since November 2022.

Separate data released earlier in the week showed the consumer price index climbing a bit more than forecast in October. Taken together, Goolsbee said, the reports indicate the Fed is losing ground on its 2% inflation target.

'We've been above 2% for almost six years,' he said, adding that 'lately we're not making any progress, and if anything, it's going the wrong way.'

Goolsbee said inflation is rising and described it as 'far more persistent than we predicted' when supply shocks first hit. He also pointed to what he called 'old-fashioned demand overheating' coming from the artificial intelligence data center building boom, which he said 'looks like it's starting to spread out of its lane.'

Financial markets have responded to the string of hot readings. Traders are fully pricing in a quarter percentage point interest rate increase when the Federal Open Market Committee next meets on Dec. 8 and 9, and they see a better than 10% probability of a larger half point hike, according to CME Group's FedWatch gauge of futures markets.

Goolsbee is not currently a voting member of the FOMC but is scheduled to become one in 2027. Earlier this week, Fed Governor Christopher Waller signaled he would be willing to consider a 50 basis point move depending on how the latest inflation data came in.

Goolsbee declined to speculate directly on whether the Fed needs to be more aggressive. 'It's all going to be about this question: What is happening to inflation, and are we on path back to 2%?' he said. 'My feeling is, right now we're not.'