The Federal Reserve has made significant inroads on bringing inflation back down to its 2% target and if that continues attention will turn to how long to keep interest rates at current levels, Chicago Fed Bank President Austan Goolsbee said on Tuesday.

"Over the next couple of months, we might equal the fastest drop in inflation in the last century," Goolsbee said in an interview with broadcaster CNBC. "So we're making progress on the inflation rate.

"And as long as we're making progress, as I've been saying for a while, the moment of arguing how high should the rate go is going to fade to how long should we keep rates at this level as inflation is coming down."

The U.S. central bank last week kept its benchmark interest rate unchanged at between 5.25% and 5.50% but kept the door ajar to raising borrowing costs further to get inflation back down to its 2% target amid a resilient economy.

(Reporting by Lindsay Dunsmuir; Editing by Andrew Cawthorne)