(Reuters) -Federal Reserve Bank of Chicago President Austan Goolsbee said Tuesday if inflation cools off the central bank has some space to cut its interest rate target.

"I think eventually, at a gradual pace, rates can come down a fair amount if we can get this stagflationary dust out of the air," Goolsbee said in an interview with CNBC.  In terms of where the Fed can go versus its current target rate range of between 4% to 4.25%, Goolsbee said a neutral rate is something like 100 to 125 basis points lower than that, noting "ultimately the rate might settle around 3% with inflation at 2% and I'm comfortable with that, with that as a marker."

Goolsbee, who is a voting member of the interest-rate setting Federal Open Market Committee, spoke after last week's decision by the central bank to cut its target by a quarter of a percentage point. While officials remain worried about overly high levels of inflation, they are also seeking to offset risks to the job market by lowering the cost of short-term borrowing. 

Goolsbee said in his TV appearance that when it comes to Fed policy, "I think we are restrictive, mildly restrictive." 

He also noted inflation risks remain real. "With inflation having been over the target for four and a half years in a row and rising, I think we need to be a little careful with getting overly upfront aggressive" with interest rate cuts. But he added "the labor market continues to cool at a sort of a mild to modest pace." 

The Chicago Fed released a report Tuesday offering what it hopes is a real-time read on unemployment, which projected the unemployment rate most likely held steady in September at 4.3%.