The economist was among the six members of the bank's Monetary Policy Committee who voted last week to keep interest rates at 5.25%, while two officials voted for a hike and one voted for a cut.
Pill said cuts from the current 16-year high of 5.25% could happen if inflation falls in line with expectations this year.
In a webcast Q&A, he said: “Lower interest rates are a reward to the economy for better inflation performance. It is the focus on when, rather than if, I think, that has been what the governor has tried to focus on.”
Governor Andrew Bailey has signalled that the central bank was ready to start easing policy, but not until it had more evidence that inflation was heading in the right direction.
"The debate has a bit shifted toward asking: 'when is the point when we will have seen enough accumulated evidence that ... we can begin to reduce the level of restriction in monetary policy in the economy and start to cut Bank Rate?'," Pill said.
"It is the focus on 'when' rather than 'if' that has been what the governor has been trying to focus on," Pill added.
The key measures the BoE is looking at are wages and services prices. He highlighted that they do not need to be back down at the target 2% level because interest rates are already “restrictive,” meaning they are suppressing activity and prices.
“We don’t need to see inflation get back to 2% on a on an underlying basis in order to begin to reduce bank rate because we’re at a restrictive level. We can reduce bank rate a little bit and monetary policy would still be restrictive,” he said.
Inflation has come down significantly from peaks of more than 11%, currently standing at 4%.
However, the Organisation for Economic Co-operation and Development (OECD) on Monday said the UK faces the highest rate of inflation in the G7 this year and next.