"And potentially if there are recommendations the Government is not ruling out adopting those recommendations or allowing the Reserve Bank to do it.
"We've already done that before with [loan to value] ratios and there are other options."
The Labour Party warned that such a policy would create yet another hurdle for first-home buyers.
Mr Key said he would not want to lock people out of the housing market.
But he added: "One of the ways to make sure they can get into the housing market is to ensure that the rate of increase isn't too fast for too long."
Mr Wheeler said the Reserve Bank would be consulting with the Government about potential responses to house price rises.
He stressed that the bank had not yet decided whether it would take further action, or what sort of action it would take.
Speaking to a select committee this afternoon, Mr Wheeler said the average house price in Auckland was now nine times larger than the average income, up from 6.5 times the average income just before the Global Financial Crisis in 2007.
"Nine makes them on that ratio one of the most expensive cities in the world," he said. "The concern I think is that the ratio could continue to increase."
Across the rest of the country, the price-to-income ratio was 5.3.
House price inflation had fallen to about 12 per cent, down from 27 per cent in September. But this was still much higher than income increases in Auckland of between 3 and 5 per cent, Mr Wheeler said.
Deputy governor Grant Spencer would not say whether potential income-related restrictions could apply only to Auckland or to investors.
But he said his preference was for a broad-based measure.
Labour MP Phil Twyford said that applying the policy to everyone would punish first home-buyers and people in the regions.
He asked why the bank could not apply a more targeted approach, such as loan to value (LVR) restrictions which focused only on Auckland or on investors.
In his regular update on the economy, Mr Wheeler said "imbalances" in the housing market were increasing.
While house price inflation had cooled off in late 2015 and early 2016, it now appeared to be heating up again, he said.
House prices were not only rising in Auckland but in the regions, in particular Hamilton and Tauranga.
"The bank remains concerned that a future sharp slowdown could challenge financial stability given the large exposure of the banking system to the Auckland housing market," he said.
"Further efforts to reduce the imbalance between housing demand and supply in Auckland remains essential."