New Zealand First leader Winston Peters this week proposed a plan to float shares in Kiwibank, with their sale restricted to New Zealanders.
All the Government's business, worth $55 billion a year, would go through the bank.
However, Mr Jackson said if the bank was sold or privatised, "fees and charges would go up".
"They would need standalone buildings, and they would have to be paid for," he said.
As long as the bank was a state-owned enterprise it was government-guaranteed.
"If it is sold or privatised the only guarantee would be Dr Cullen's guarantee, and in my view that would be political rhetoric," he said.
Mr Jackson said he had asked the duty manager at Kiwibank in Alexandra if he could leave a petition at the bank.
The duty manager had promised to talk to the bank's head office and would let him know the answer next week.
Mr Jackson said the petition would be available in Alexandra for a couple of weeks.
If the petition proved popular, he hoped to send it around the country after that.
