Former National Party president Michelle Boag added having five vying for the top job would drag the contest out and cause division among the ranks.
"A fragmented support base in caucus will make it more difficult for them to come together because you have three pretty even camps. You will end up with one winner so two-thirds won't be happy."
The prospect of five candidates for Labour's top job saw the party lambasted on Twitter yesterday.
Herald columnist Toby Manhire Tweeted: "If Parker and Shearer both join the Labour leader race, that's more than 15% of caucus standing. #toomanydavidsonthedancefloor."
Parker will announce his tilt at the leadership today, the Herald on Sunday undertsands.
He had first intended to run for the leader's role against Cunliffe in 2011 but pulled out after Shearer also put his name in, citing personal reasons as a factor.
Parker's partner is Barbara Ward, the former partner of singer Chris Knox. Ward still provides care for Knox since his debilitating stroke in 2009.
The pair were reluctant in 2011 to open their relationship to the public scrutiny that comes with the leadership role.
Parker's decision to stand this time indicates that has changed. Ward is actively involved with the Labour Party, she works for MP Jacinda Ardern and helped organise Labour's annual conferences.
Parker is highly respected within Labour and his supporters believe he is best placed to ease the tension between caucus and members, unify caucus and get Labour back in front of the voters' eyes for the right reasons. He was deputy to Cunliffe over the past term and was loyal - but was angered by Cunliffe's response to the election result.
Parker's entry makes it almost inevitable the contest will not be decided on the first round of votes. Labour has a preferential voting system for its leadership under which members, caucus and affiliates rank candidates in order of preference.
In each round the lowest-ranked candidate is knocked out and their supporters' second preference votes are tallied up until one candidate has more than 50 per cent.
Nominations for leadership close on Tuesday, and a leader will be chosen on November 18.