He also pointed to Labour and Greens' fundraisers and donations, such as the $125,000 given to the two parties by Les Mills CEO and green growth advocate Phillip Mills.
Dr Norman said today that paying cash to get access to Government's inner circle was "not normal".
"This is party fundraising with access to ministers at its heart. It is democracy for sale, and it is worlds away from legitimate forms of party fundraising.
"The Green Party does not believe that the Cabinet Manual sanctions this behaviour or that Ministers are attending Cabinet Club outside their ministerial roles."
He added: "Ministers attending Cabinet Club events are advertised, by their colleagues, as attending in their ministerial capacity.
"Those who pay Cabinet Club memberships clearly expect access to Ministers with real power, not backbenchers or members of the opposition."
The Greens wanted Government to introduce a ministerial disclosure regime, which showed how often ministers met with donors and what they discussed.
Immigration Minister Michael Woodhouse revealed yesterday that he had attended a Cabinet Club meeting last year and discussed immigration policy with Chinese attendees.
He said he discussed immigration at nearly event he attended, and did not believe it was inappropriate.
Greens' criticism of the Cabinet Club events comes follows broader scrutiny of National ministers and their relationships with party donors.
Justice Minister Judith Collins has been attacked for weeks in the House about her dealings with milk exporter and National donor Oravida, which has her husband on its board.
And National MP Maurice Williamson resigned his ministerial warrant last week after appearing to interfere in a police case on behalf of another National donor, Chinese businessman Donghua Liu.
Mr Liu had asked Mr Williamson and other ministers to help relax immigration rules for business migrants.
Mr Woodhouse confirmed he had met with Mr Liu last year.
The minister said he had no plan to change the Investor Plus category, which required non-English speaking migrants to invest $10 million to get New Zealand residency.