Last month, Regional Facilities boss Robert Domm backed down after protests by art patrons on a plan unveiled in April to scale back Mr Saines' role and focus on the gallery making money.
Now the council body is taking a hard look at the gallery's operations. A report dealing with possible savings is expected to be discussed by the Regional Facilities board behind closed doors next week.
Neither Regional Facilities nor Mr Saines wanted to talk specifics yesterday.
But Regional Facilities' chief finance officer Patrick Cleaver warned councillors last week of reducing gallery patron satisfaction levels.
Mayor Len Brown's 10-year budget has set savings targets for all council-controlled bodies to achieve an overall rates rise of 3.6 per cent.
For Regional Facilities, this means trimming spending by $3.8 million, which a spokesman called a "challenge" but not one that would affect permanent staffing levels or important public facilities.
All Regional Facilities businesses, which include the art gallery, museum, zoo, Aotea Centre and Mt Smart Stadium, have been asked to come up with savings.
Motorists face paying millions more for parking in central Auckland streets to help Auckland Transport meet a $45 million deficit in operating expenditure.
And Waterfront Auckland has indicated cutbacks in the maintenance of parks and public spaces.
Yesterday, a council spokeswoman said council-controlled bodies had been told to produce savings of $15 million a year, or $150 million over 10 years. This was in addition to $1.7 billion of savings by the council.