"I haven't seen anything that says that's wrong - that is on the golden path" of bringing inflation down to 2% without causing a recession, Goolsbee said in an interview on CNBC. "That would be a Fed triumph and that can involve a couple of rate increases over this year."

The Fed held its policy rate steady last month, targeting a 5%-5.25% range, but two-thirds of policymakers signaled they expect at least two more rate hikes by year's end, given still unacceptably high inflation. Remarks from Goolsbee previously sounded more skeptical of the need for further rate hikes on top of what the Fed has already done.

A government report earlier Friday showing employers slowed hiring in June but the labor market remained tight, with unemployment ticking down to 3.6% and hourly wages rising at a 4.4% annual pace.

The report is suggestive of labor market cooling, Goolsbee said, and the full effect of the Fed's 500 basis points of rate hikes since last March is still to come. But, he said in words that echoed those of his Fed colleagues, inflation is still too high.

"The Fed's overriding goal right now is to get inflation down," Goolsbee said, adding that he believes it can be done without pushing unemployment up to levels that would mean a recession.

Financial markets are pricing a Fed rate hike when policymakers next meet, in two and a half weeks.

Goolsbee said his mind is still not made up for that meeting, with key data on June inflation still to come before then.

Unlike many of his Fed colleagues who say that progress on services inflation is critical to the Fed's inflation fight, Goolsbee said his eye is on goods prices, which pre-pandemic typically trended flat or downward. Services inflation even pre-pandemic was typically higher than the Fed's 2% goal, he said.

"Let's keep our eye on the goods inflation number to figure out if we're still on the golden path or not," he said.