The Prime Minister makes $428,500 a year.
The final three are current Deputy Commissioners Mike Bush and Viv Rickard, and Assistant Commissioner Dave Cliff.
Senior police spoken to by the Weekend Herald said all three candidates could do the job, but there was a clear favourite.
"Most staff want Mike Bush," said one officer. "He's a polished, natural leader with the X-factor - very sharp.
"He is an accomplished investigator who has led a number of high profile investigations, a highly successful proven leader and he is liked and respected by all staff at all levels.
"He's calm and collected, never loses his cool."
Mr Bush came under fire last year following his speech at the funeral of retired Detective Inspector Bruce Hutton, found by a royal commission of inquiry to have planted evidence used to wrongly convict Arthur Allan Thomas of the murders of Harvey and Jeannette Crewe.
Mr Bush told mourners Mr Hutton had "integrity beyond reproach", souring public opinion of him and leaving many questioning whether he had affected his chance of becoming commissioner.
But colleagues stood by Mr Bush, saying he was the "architect and driver" of the new police "prevention first" operating model and had served in most roles within the organisation meaning he had a deep insight into the job.
Said one: "Viv and Dave could both do the job. Viv, there's nothing he does not know about the business. Dave has not really been tested in roles at a higher level like Mike and Viv. The exception is the Christchurch quake but was a bit of an unknown before that.
"He's currently assistant commissioner (road policing); it's bit of a big leap to commissioner."
Another senior officer thought the application process was a "two horse race" between Mr Bush and Mr Rickard, who were both effective leaders.
"I think you will get a reasonably even lot of views with Mike possibly having more support in the north and Viv in the central/south."
A third high-level officer praised Mr Rickard and hoped he would be named the new commissioner.
"Viv is a leader - astute, respected, a top negotiator with excellent interpersonal skills and a damn hard worker," he said.
The Police Commissioner role combines two positions, chief constable and chief executive. The chief constable heads the police force and is responsible for all policing and cases as well as assets and a budget of more than $1 billion.
The application process for the position is run by the State Services Commission on behalf of the Prime Minister and Police Minister.
Police spokesman Ross Henderson refused to say what date the current commissioner's tenure would end.
Viv Rickard Deputy commissioner (resource management)Joined the police in 1985 and appointed to his current role in May 2010. Previously he was assistant commissioner of operations and assistant commissioner of crime and investigations. He served in both general and investigative branches before becoming part of the Police Executive, when he was appointed district commander for Northland in 2001. Other roles have included two years as district commander in Waitemata and national manager for crime and investigations.
Mike Bush Deputy commissioner (operations)Joined the police in 1978. His operational and administrative positions include Southeast Asia liaison officer, based in Bangkok, when he was the first New Zealand official to reach devastated Phuket after the 2004 Asian tsunami. He was made a Member of the New Zealand Order of Merit for his role in this operation. As Counties-Manukau district commander he oversaw deployment of an additional 300 officers in New Zealand's busiest police district, and pioneered neighbourhood policing. He was appointed to his current role in 2011.
Dave Cliff Assistant commissioner (road policing)Joined the police in 1983, and held positions including national road policing manager. He worked in Vietnam as part of a New Zealand Aid project, and in Buenos Aires, Argentina, advising on road safety issues. He was appointed Canterbury district commander in 2007 and became familiar as the face of policing after the Canterbury earthquakes. He was appointed assistant commissioner (south) in May 2011 and to his current position in November 2012. He was made an Officer of the New Zealand Order of Merit in 2012.
