Chicago Fed President Charles Evans said on Monday that the interest rate hike should be very gradual when the Fed will start raising its interest rates.

"After lift-off, I think it would be appropriate to raise the target interest rate very gradually. This would give us sufficient time to assess how the economy is adjusting to higher rates and the progress we are making toward our policy goals," he said.

"And right now, regardless of the exact date for lift-off, I think it could well be appropriate for the funds rate to still be under 1 percent at the end of 2016," Evans added.

Chicago Fed president noted that he is not confident if the inflation target in the U.S. will be reached "within a reasonable time frame".