A senior was quoted as saying it was a two-horse race between Bush and Rickard, both of whom were 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," he said.
Another hoped the job would go to Rickard, who he described as a leader, astute, respected, a top negotiator with excellent interpersonal skills and a "damn hard worker".
It is not known when Mr Marshall's tenure will end, although it will be this year.
Mr Rickard, who joined the police in 1985 and was appointed to his current role in May 2010, was previously Assistant Commissioner of operations and of crime and investigations. He served in both general and investigative branches before becoming part of the Police Executive, when he was appointed Northland District Commander in 2001.
He has also served (for two years) as Waitemata District Commander and national manager for crime and investigations.
Mr Bush joined the police in 1978, his career including service as South-East Asia liaison officer, based in Bangkok, when he was the first New Zealand official to reach Phuket after the 2004 Boxing Day tsunami. He became a Member of the New Zealand Order of Merit for his role in that operation.
As Counties-Manukau District Commander he oversaw the 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.