Mr Barnett, like Mr Banks, has still to make a final call to line up against Mr Brown, who has been plagued by a sex scandal and criticised for his handling of the city's finances.
Mr Brown - a Labour Party member - refused to be interviewed about his political future, but in a statement said he was focusing on the job at hand rather than events two years down the track.
As well as competition from the right, the mayor is under pressure from his increasingly popular deputy, Penny Hulse, who has expressed interest in the top job, but said she would never stand against Mr Brown.
This year, Ms Hulse has been on a health kick, made a big impression standing in for Mr Brown for a month, and lifted her profile at city events and in social media.
A Labour source said Mr Brown was "rooted" and if he couldn't win he should step aside for someone who could.
Labour had given considerable help to Mr Brown at his last two elections. But the party was still smarting at the mayor not backing the workers in the ports dispute, the source said, and without the party's help he would have to put up his own billboards and deliver pamphlets.
Former Labour Party leader and Mt Roskill MP Phil Goff said it would be improper for him to advise or pressure Mr Brown about his future.
"I have known Len for a long time. I have a personal regard for him. He's had a tough time, but he has got to determine what he thinks he can now achieve in politics and whether or not he contests [the next] election," he said.
Mr Goff said he'd received numerous approaches from across the community to stand for the mayoralty "but I don't think it's where my career is taking me at the moment".
"I haven't ruled it out completely but nor have I given it serious consideration," he said.
Mr Banks, who lost to Mr Brown by 66,000 votes in 2010, said if he stood again with the right team and right policy mix "I would beat him every day of the week".
"I'm appalled at the direction of this big-spending mayor. It's only a matter of time before ratepayers can't afford it and the city will go broke."
Mr Banks said if he did stand he would put together a progressive team across the political spectrum to "relaunch the Super City".
"It will never be about me - but about getting the right leadership," he said.
Mr Barnett, aged 65, said he was as fit as he was before he withdrew from standing for a seat at the first Super City elections in 2010 after being diagnosed with throat cancer. He made a full recovery.
The Karaka resident said it was too early for policies, but favours a more businesslike approach to investing in the city and getting Aucklanders to better understand and participate in city life.
"The story telling of what council does and why is being poorly told by the council," said Mr Barnett, who cites the lack of understanding about the benefits of the city rail link, which he supports.
The search for a candidate to take on Mr Brown is an ongoing problem for the centre-right in Auckland, which has struggled since the emergence of the Super City.
The once powerful Citizens & Ratepayers brand under the old Auckland City Council has all but disappeared, and there is little cohesion among right-leaning councillors. The same goes for the left.
Orakei councillor Cameron Brewer, the most effective opposition voice around the council table, is widely expected to step down in 2016 to focus on a new PR business venture with Carrick Graham, of Dirty Politics fame, and Ricardo Simich.
He is also focusing on a new, young family.
It was "never my intention to be mayor", said Mr Brewer, adding he might stand for Parliament one day or return to local politics.
Former National Party president Michelle Boag has been on the hunt for a candidate, with rumours she has two people in her sights.
Orakei Local Board member Mark Thomas has also been having conversations with Local Board members and others all year to find a mayoral candidate who can promise less and deliver more. So far, no one has emerged.
John Palino, the novice politician who stood against Mr Brown last year and attracted 109,000 votes, is not ruling out another crack at the mayoralty in 2016.
Mr Palino continues to insist he had no knowledge of Mr Brown's affair with council adviser Bevan Chuang, who had links with the Palino camp and met with the right-wing candidate in a Mission Bay carpark two days before the affair was made public.
Another possible candidate, National MP for Pakuranga Maurice Williamson, who toyed with standing for the mayoralty last year, did not respond to phone messages.
Councillor Chris Fletcher, former National MP and Auckland City Mayor, is losing confidence in Mr Brown but not of a mind to challenge him in 2016, saying the civic duties alone are too time-consuming.
But if the mayor stuck with his "unaffordable" draft budget, she said, there would be people thinking long and hard over the Christmas break about getting the city back on track.
Among the new councillors, Chris Darby is a growing force and independent thinker challenging the status quo on issues like transport and waterfront development.
The former North Shore city councillor has no mayoral ambitions, but does eye a senior role, possibly deputy mayor, under an "imaginative mayor" with a bold, forward-thinking vision for Auckland.
"One of the most influential positions you could take is to sit behind a powerful mayor," he said.
