The cost of NZ Super is expected to triple in the next 20 years from $11 billion to $36 billion as more people reach the over-65 age-group and live for longer.
Any prospect of reform stalled under Key, who said he would resign rather than tighten eligibility rules.
But the Retirement Commissioner Diane Maxwell is among those wanting change to avoid "painful decisions" in future. Maxwell said in December the eligibility age should be raised gradually, Government contributions to the Fund should restart, and the residency requirement raised from 10 years to 25 years.
A spokesman for English told the Herald today it was too early to give specifics about his plans for superannuation.
Labour leader Andrew Little said today that Super entitlements were a very sensitive subject, and English's comments would worry New Zealanders.
"To continue with very vague language is at the very least clumsy, but will also cause considerable anxiety."
Little wants the eligibility age to stay the same but has promised to resume contributions in his first Budget if in power. Labour previously campaigned on a higher eligibility age but Little scrapped that policy when he became leader.
New Zealand First leader Winston Peters said he supported tighter rules for older immigrants, citing figures of 86,000 people who had claimed Super in the last 15 years after just 10 years in the country.
Peters said English was the latest to make "alarming noises" about the affordability of the NZ Super. The scheme was relatively affordable by OECD standards but New Zealanders were being "railroaded" into thinking it was unaffordable, he said.
However, the Herald's former economics editor Brian Fallow warned Super's costs were forecast to "head north" to unaffordable levels - 7.9 per cent of GDP by 2060.
English was right to review the cost of NZ Super, he said, but raising the age of eligibility alone would not be enough to address rising costs. The Government would also need to either introduce means-testing or change the way Super payments were calculated. At present, payments are tied to the average wage.