"The last thing he needs is a deputy mayor quietly kneecapping him in the background. That is not something I would do," Mrs Hulse said.
The 57-year-old Waitakere councillor has been praised for stepping up for Mr Brown over the past month, dealing with the power blackout, the closure of two water dams after a herbicide scare and standing alongside Prime Minister John Key at the Diwali festival.
Right-leaning councillor Cameron Brewer said on social media she had "shone in the role" and there had been a much better vibe around the council while Mr Brown was away, to which Mrs Hulse replied: "Thanks Cameron."
The left-leaning Waitemata Local Board chairman Shale Chambers and fellow Waitakere councillor Linda Cooper agreed with Mr Brewer's assessment of Mrs Hulse's performance.
Mrs Hulse's interest in the Super City mayoralty is a double blow for Mr Brown after a family holiday in Europe.
On Mr Brown's return to work, there was a letter signed by all 21 local boards expressing frustration and anger at a mayoral budget proposal containing big cuts to community projects and services.
"We have witnessed cuts in funding for local priorities," said the board chairs, adding "community-based innovation has been stifled".
The letter highlighted a proposal by Mr Brown to slash $1.3 billion in spending on parks, community and lifestyle.
"This is of key interest to local boards ... we know that our communities value local facilities, parks and events for the liveability of their neighbourhood and to help build strong and inclusive communities," the letter said.
Mangere-Otahuhu Local Board chairwoman Lydia Sosene did not want to criticise "south side boy" Len Brown (a former Mayor of Manukau) but said the budget process was "really, really tough".
A wishlist of 50 projects the local board wanted for its deprived communities had been narrowed down to three capital projects over the next decade, she said.
An official said the mayor and councillors will continue discussions with local boards next week and take their feedback into account on decisions on the 10-year budget.
Len's holiday blues
• Len Brown returns from month-long holiday.
• Deputy mayor Penny Hulse praised for stepping up.
• Mrs Hulse not ruling out tilt at mayoral chains.
• Mr Brown faces revolt by local boards at budget cuts.