The confidence and supply agreement between the National Party and the Act Party includes the implementation of this proposal within this parliamentary term.
A Ministry of Health briefing paper released under the Official Information Act showed that it was being considered ahead of the next wave of welfare reforms.
A spokeswoman for Ms Bennett said encouraging immunisation was on the table but no decision had been made.
In October 2010, a select committee made 30 recommendations on how to improve immunisation rates.
In March, officials reported to Health Minister Tony Ryall about progress on the final six recommendations.
The briefing paper, written in March, said the Ministry of Health would work closely with the Ministry of Social Development over the next three months "to explore further opportunities for incentivising parents and providers to ensure children receive their schedule immunisations".
At present, immunisations are not compulsory.
While not raised by the Ministry of Health or the minister, the Welfare Working Group suggested that if a beneficiary did not comply with health checks for their children, it would result in their income being managed by a third party or other means, such as a payment card.
Co-leader of the Green Party Metiria Turei said the state did not have the right to use financial pressure on parents to force them to immunise their children.
" ... This is an extension of the approach to contraception and exactly the sort of slippery slope we have been warning against."
Ms Bennett's office would not confirm whether the incentive would be rolled out in the next reform announcement, expected in August.
The No Forced Vaccine Group coordinator Katherine Smith said the confidence and supply agreement and the recommendation from the committee were ambiguous and lacked detail. "I think it is an insult to vulnerable people for the Government to consider any legislation that infringes on parents' rights to decide freely whether they want their children to have either or all recommended vaccinations."