The texts were between Wayne Brown and the Transport Minister.
Currently, nearly a quarter of kerbside material collected in Auckland is contaminated.
The Auckland Mayor also expressed annoyance at central Government "foisting" consultation onto the 10-year budget process.
"$600,000 is plenty by any measure and certainly money is not my personal motivator."
Councillors have been asked to double-check whether they or their spouse owns shares in the airport.
Julie Fairey, an Auckland Councillor, may soon vote on the council's sale of shares in the company.
"One way or another we have to bridge the gap."
Councillors received a budget update this morning, ahead of approving the annual budget next month.
Brown didn't front for the report into the review of the Council's flood response.