Andy Burnham is said to be on the brink of a 50/50 decision on how to keep PC Harper's killers behind bars.
The Prime Minister is thought to have been handed two plans by civil servants - both of which would see the vile duo stay behind bars.
Jessie Cole and Albert Bowers had been set to run free on Britain's streets under Labour's early release scheme - despite Mr Burnham's partial U-turn.
But a petition to stop them seeing their freedom early has surpassed a staggering 800,000 signatures already.
Now, Mr Burnham faces two choices, according to The Telegraph, which revealed on Friday he would "explore every option" to lock the pair up.
He could block the release of all inmates responsible for the death of emergency service workers.
Or, he could block the release of all inmates convicted of manslaughter.
The Prime Minister is believed not to have decided on which of the two options to pick.
He is set to make his choice within the next few weeks. Then, ministers can publicly make changes to the controversial release scheme.
Both choices come with significant concerns.
There are fears keeping every prisoner convicted of manslaughter behind bars would place too much pressure on the country's notoriously overcrowded jails.
While there are about 950 of those currently behind bars, the number eligible for early release would be lower as some of that number will also have been sentenced for other, more serious offences.
However, the number of those convicted of killing emergency workers is said to be significantly lower - meaning fewer people overcrowding the prisons, but the manslaughter inmates would be out on the streets.
There is a second problem in the second option: Singling out police killers could lead to legal action.
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Given there is no single charge for manslaughter of an emergency service worker, it may be deemed preferential treatment by the rest of the manslaughter inmates.
The PC Harper case and Labour's early release scheme has handed the Prime Minister his largest headache yet during his short stint in No10.
And this week, he will embark on a "national tour" to ask the public how the Government can improve their lives.
He is expected to unveil a series of measures intended to help with bills and will focus on improving high streets.
Officials said he would use the summer tour to inform his 10-year plan for the country.
A Ministry of Justice spokesman said of the PC Harper case: "The death of Pc Andrew Harper was a horrific crime. Our thoughts are with his family and friends, and we share the anger from the police community that we are in this position.
“Thanks to tireless campaigning by Andrew’s family, Harper’s Law means that anyone convicted of killing an emergency worker whilst committing a crime now gets a mandatory life sentence.
"This Government has gone further by introducing a presumption that anyone convicted of murdering a police, prison or probation officer is handed a whole-life order.
"We have been clear that we wanted to go further and block more offenders from getting out sooner into their sentence but could not do so without risking prisons reaching capacity and collapsing.
"If that happened, police could not make arrests, courts could not remand offenders and there would be unchecked criminality on our streets."
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