The decision follows warnings from officials about the approximately £2billion price tag for taxpayers needed to sustain the utility over 18 months under a Special Administration Regime.
Concerns were also raised regarding potential legal challenges and practical obstacles to such a move.
Mr Burnham has consistently maintained that bringing Britain’s biggest water supplier into public hands remains the preferred outcome.
Andy Burnham has reportedly shelved plans to put Thames Water into administration
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However, the Labour Government is still assessing whether administration represents a workable path forward, a process expected to stretch over several months, The Times reports.
Thames Water has been weighed down by roughly £20billion in debt, leaving the company in a precarious financial position.
The utility has struggled to stay afloat for years, with a succession of owners failing to channel sufficient funds into its deteriorating infrastructure.
When the news broke later last night, neither the Government or Thames Water offered immediate comment on the latest developments.
Thames Water has 16 million customers and 8,000 employees | PA
Andy Burnham is having to make tough economic decisions
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A consortium of senior creditors operating under the name London & Valley Water put forward a competing rescue proposal in July, designed to steer Thames Water away from state control.
The revised plan centres on a ten-year transformation programme aimed at overhauling the beleaguered utility.
On Monday, the group unveiled its first slate of proposed directors who would guide the restructuring if the plan gains approval.
The proposal also floats the possibility of granting the government a “golden share” in the company, a mechanism intended to address Burnham’s push for public ownership while keeping Thames Water out of administration.
Thames Water chief has previously urged Andy Burnham to provide clarity
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Russ Mould, an investment director at AJ Bell, said: “In an attempt to see off a possible nationalisation, Thames Water creditors have unveiled plans for a big refresh.
“The former head of Yorkshire Water, Liz Barber has been lined up to join the board along with two alumni from broadband infrastructure business Openreach and a former senior civil servant in Bernadette Kelly.
“The hope being that these are the sort of credible names which can inspire confidence in the company’s future in private hands.”
GB News has contacted both the Government and Thames Water for comment.