The Government has come under pressure from medical professionals to introduce a sugary drink tax, particularly after the British Conservative Government opted to do so in its latest Budget.
But although the Greens want such a tax brought it, Labour's position has been that there isn't enough evidence.
King has since suggested that position could change.
She told the Herald that no final decision had been made, but evidence for a sugary drink tax continued to mount.
``And I think there is growing support for such an approach. So I am reading all I can and talking to people.
``I hope to have the rest of our obesity policy ready for November.''
In January the World Health Organisation recommended that governments tax sugary beverages to reduce childhood obesity.
The commission - co-chaired by the Prime Minister's chief science adviser Professor Sir Peter Gluckman - cited research by Mexican health officials on the 10 per cent surcharge on sugary drinks that was introduced there three years ago.
Health advocates and some Mexican senators are now urging for that tax to be doubled, as sales of fizzy drinks have largely recovered after an initial drop.
About $3.45b has been raised through the Mexican tax.
Soft drink producers argue such taxes have little to no impact on consumption, and their products are not a major cause of obesity.
New Zealand has the developed world's third-highest rate of children who are obese or overweight. The rates are higher in poor areas and for Pacific and Maori children.
Health Minister Dr Jonathan Coleman has rejected calls for a sugary drinks tax.
Instead, the centrepiece of the Government's new childhood obesity plan is to have 95 per cent of children identified as obese in the Before School Check of 4-year-olds to be referred to a health practitioner.