Johann Lamont's party has also exempted sitting List members from gender-balance rules, following pressure from the Labour group at Holyrood.
Simon Pia, who was former leader Iain Gray's spin doctor, said the party was seen as being full of "vested interests".
Labour's defeat at the 2011 Scottish Parliament election prompted a rethink of the party's structure, governance and operations.
Part of the agenda was supposed to be selection reform, which meant getting a better calibre of candidate.
In 2011, Labour returned 15 MSPs in constituencies and 22 members on the regional Lists, some of whom were deemed to be of poor quality.
One senior party source was more blunt: "A small minority of the List MSPs are just rubbish."
List MSPs get re-selected if they survive a trigger ballot. If they pass, the MSPs are guaranteed the top rankings on the List and cannot be leapfrogged by party members.
But the party last year recommended scrapping the system of "protected places" enjoyed by List MSPs. Labour instead proposed allowing any party member to run for the top spots.
The plan went down badly with sitting MSPs who feared their jobs would be at risk if they faced a challenge from members.
The Sunday Herald has learned however that the plan was axed by the party's Scottish Executive Committee earlier this month.
Critics believed it would create a two-tier system whereby List MSPs would face a challenge, but constituency members would not.
It means the MSPs described as "deadwood" by one insider have a decent chance of getting re-elected in 2016. The party also proposed last year that regional Lists should be twinned on a gender basis.
In another change of heart, the party hierarchy decided that this rule should apply only to List candidates other than sitting MSPs.
Pia said: "Labour has to be more open and inclusive and a start would be with who its candidates are. Of course there is a place for long-term experience but being a MSP is about public service, not a job for life. New blood must get a chance and competition would be healthy.
Primaries are something the party should not be afraid of. The Left has introduced them in France and Italy so why not here? Scottish Labour had been stuck in a rut since 1999 and it has suffered for being seen as too closed, bureaucratic and full of vested interests."
SNP MSP Aileen McLeod said: "No matter what Labour in Scotland tries to do with its selection processes, it is their policies they will be judged on. The people of Scotland will not back Labour's anti-independence alliance with the Tories, and leader Johann Lamont's plans to cut the public services delivered by the Scottish Parliament while supporting wasting billions pounds on Trident."
A Scottish Labour spokesman said: "Our new selection procedures will give our rank-and-file members the power to choose the candidate they believe will do the best job of representing their communities while our twinning system will mean Scottish Labour once again leads the way on gender equality.
"By ensuring our candidates are selected by our constituency parties, and our team for 2016 reflects the modern Scotland we live in, we believe these are the fairest, most democratic and equal selection procedures of any of the leading Scottish parties."
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