Gatland says he will step down after the 2019 Rugby World Cup.
The 52-year-old hopes to coach in his homeland once that deal expires and Brooke says he could be a candidate for the national side by then.
"Warren Gatland's certainly got the capabilities of dealing with that," he said.
"It's all about managing the players and he's been an All Black himself, so he knows what's required of a player.
"His coaching credentials have been built through coaching in the UK. He's a quality guy and a very good coach."
Two of Gatland's Wales predecessors and fellow countrymen, Sir Graham Henry and Steve Hansen, went on to coach the All Blacks.
Hansen emulated Henry's exploits of 2011 by guiding New Zealand to a third World Cup with victory over Australia in the 2015 final.
His contract expires in 2017 and Hansen expects to step down before New Zealand defend their title two years later.
Since taking over in December 2007, Gatland has led Wales to two Grand Slams and become the longest-serving coach in their history.
His deal expires after the tournament in Japan and he plans to return to his homeland, where he previously coached his native Waikato after spells with Ireland and Wasps.
Waikato Chiefs chief executive Andrew Flexman says Gatland would walk into a job in Super Rugby.
"He's about as credentialed as you can get and certainly in Chiefs country he's considered to be right up there," Flexman told BBC Radio Wales Sport.
"We're pretty excited to hear that he's interested in rounding out his coaching career in this country.
"Depending on what the lie of the land looks like for us in the future, we'd certainly engage him in a conversation around that."

Arun District Council said the plans for Bognor Regis also included student accommodation, car parking and an access road from Felpham Way.
The university's digital technology and engineering department will move to the site if permission is granted.
It was awarded Â£8m funding from the government last year.
The technology park will have places for 500 undergraduate and postgraduate students per year.
The council said the six-storey student accommodation building, to the north of the proposed five-storey teaching block, will provide 171 bedrooms.
The site, next to the Upper Bognor Conservation Area, has been classified in the Arun Local Plan since 2003 as an area of expansion for the university.
The public has until 7 April to comment on the plans, which will then be considered by councillors.

The Online Hate Crime Hub is made up of five specially trained Met police officers who will try to identify, prevent and investigate online abuse.
Sadiq Khan said officers would "work with community experts to develop the police's understanding of online hate".
It is the first hub of its kind in the UK and will cost Â£1.7m over two years.
It is being funded by the Met and the Mayor's Office for Policing And Crime (MOPAC), with Â£452,000 also being contributed by the Home Office Police Innovation Fund.
Any online hate crimes reported to police in the capital, including abuse posted on Twitter and Facebook, will be looked into by the unit.
Officers will provide referrals to victim support groups and work with police in relevant boroughs to investigate.
City Hall said discussions were also under way with social media companies "to develop appropriate online sanctions for perpetrators of online hate".
Victoria Wright, a disability and disfigurement rights campaigner in London, who has been subjected to online abuse, called the hub "a much needed initiative that will make a real difference".
"It's vital that those of us who are victims of online hate crime receive a robust response from the police," she said.

The serious flooding affected large parts of county Londonderry as well as nearby Donegal.
On Wednesday morning, the flood water was still several feet high outside the Drumahoe venue after the nearby River Faughan burst its banks.
Friday's Championship game against Ballyclare switches to Dixon Park.
The expectation is that Institute will be unable to play home games at their premises for at least a month.
The club's dressing rooms are also understood to have been damaged by Tuesday's flooding which caused major disruption throughout the North West.
Pictures of the damage were put on Institute's Twitter feed on Wednesday and the club described the situation as "soul destroying".
Wales head coach Warren Gatland has the credentials to be All Blacks coach, according to ex-New Zealand forward Zinzan Brooke.
[NEXT_CONCEPT]
Plans for a new engineering and digital technology park for the University of Chichester have been submitted to the local council.
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A police unit to help tackle online hate crime and provide better support for victims in London has been launched by the capital's mayor.
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Institute's Riverside Stadium is likely to be unavailable for some time after their pitch was badly damaged by flooding on Tuesday night.