Huw Pill told the Financial Times that the Bank would have a "live" decision to make at its next interest rate-setting meeting on 4 November.
It follows recent comments from Bank of England governor Andrew Bailey who said it "will have to act" on inflation.
The UK interest rate has been at a historic low of 0.1% since March 2020.
Recent data showed that inflation growth slowed to 3.1% in the year to September. However, it is expected to increase because of rising energy costs, higher wages to fill record vacancy numbers and supply chain disruption.
Mr Pill, who succeeded the Bank of England's former chief economist Andy Haldane last month, said he would "not be shocked" to see inflation reach 5% or above in the coming months.
He told the Financial Times: "That's a very uncomfortable place for a central bank with an inflation target of 2% to be."
While Mr Pill declined to say how he would vote when the Bank's interest rate-setting Monetary Policy Committee meets early next month - stating "it is finely balanced" - he said: "I think November is live."
Separately, a survey of consumers found that a high proportion of them expect inflation to rise over the next 12 months.
GfK, the market research group, said that 48% of people it surveyed in October think inflation will accelerate, compared with 34% in September.
Joe Staton, client strategy director at GfK, said: "More and more shoppers expect that costs for goods and services will jump dramatically in the next 12 months.
"This rapid increase will impact our ability to shop and save, and our willingness to spend, at a time when our incomes are outpaced by inflation."
Tony Brown, chief executive of New Start 2020, which owns Beales department stores, told the BBC's Today programme that retailers were facing higher costs, some of which were being passed on to shoppers.
He said that the cost of a container to ship goods into the UK had risen from about $2,000 (£1,450) a year ago to $18,000.
"The wholesalers are passing those costs onto us," said Mr Brown.
He said that, for example, the cost price of a vacuum cleaner had risen from £49 last year to £79.
"So that cost price has to be passed on, we can't absorb it," Mr Brown said. "We are passing on a proportion of that and having to take a hit on the rest, so it does dilute margins.
"It is a tough time for retail out there and I think what we need more than anything is some sort of calmness in the supply chain."
Some of the world's biggest food producers have also said they have been increasing prices of their products to cope with rising raw material costs, as well as higher energy price and supply chain difficulties.
Unilever, which makes PG Tips, Cornetto, Marmite and Dove skin care, said it had lifted prices and expects that to continue into next year.
The Times reported that Unilever said the cost of palm oil, which the company uses in soap and moisturisers, had risen by 82% over two years because of labour shortages in Indonesia.
Poor crop production of soya bean oil in Brazil, which is used in food, has also led to higher prices.
Kraft Heinz, which makes tomato ketchup and baked beans, recently warned that people will have to get used to higher food prices.
And Nestle revealed this week that it too had increased prices, which rose by 2.1% in the third quarter.
The maker of Kit-Kats, Nescafé and Purina pet products said prices had risen on the back of higher energy and raw materials costs, as well as transport.