Andy Burnham’s supporters are divided over who should be his chancellor, with a briefing war breaking out between advocates of the former health secretary Wes Streeting and those close to the energy secretary Ed Miliband.

Some of those advising the Makerfield MP are urging him to choose Streeting if he becomes prime minister, in a bid to reassure the business community and fossil fuel industry.

Others however insist he must pick Miliband, whom they see as more likely to back radical policy ideas and push back against a reluctant Whitehall if needed.

The battle for No 11 could define Burnham’s time in office should he reach Downing Street, with MPs saying it will give the clearest sign yet of how radical he intends to be.

“Who becomes chancellor is absolutely key – not so much because the personalities themselves matter, but because it will give us the clearest sign of what kind of prime minister he is,” said one person who has advised Burnham in recent weeks.

The former Manchester mayor will set out more of his policy ideas in the coming weeks, but allies say he has not yet decided who his chancellor should be.

He is conscious of the need to reassure investors, given his previous comments about the UK being “in hock” to bond markets.

As part of that reassurance effort, the Guardian has learned his team have spoken to Jim O’Neill, the former Goldman Sachs chief economist and Conservative minister, about becoming his chief economic adviser – though no final decision has been taken on that role.

There is a more contentious tussle, however, over the role of chancellor, with Miliband and Streeting emerging as the two frontrunners – though with others including Yvette Cooper, Miatta Fahnbulleh, Darren Jones and John Healey also possible picks.

Many of Burnham’s allies want Miliband to become chancellor, arguing that only the energy secretary has the vision and the drive to implement some of Burnham’s more radical policies, such as bringing utilities into public control.

One said: “There is only one candidate who a) has got really serious Treasury experience; b) is a longstanding friend and ally of Burnham; c) shares his core arguments and agenda; d) has shown at the energy department he knows how to get things done and through the system. And that’s Ed.

“Regardless of politics, he is the outstanding figure for the role.”

Another added: “You cannot have someone in No 11 who does not fully buy into the prime minister’s agenda. Plus Ed [Miliband] has clearly been the most successful minister in this government – it has to be him.”

Some argue that appointing Miliband would risk triggering a bond market shock given he comes from the left of the party and has previously argued for higher borrowing to pay for green infrastructure.

One person who has advised Burnham in recent weeks said: “Miliband is in cloud cuckoo land if he thinks he would be suitable for the job. You will not find a person in the financial markets who thinks it would be a good idea.”

They added: “Wes Streeting, however, I would be on board with, he says a lot of sensible things.”

Those close to Miliband point out he spent years as an adviser and minister in the Treasury, and that his pro-green policies have been well received in the fast-growing renewables industry if not among fossil fuel companies and unions.

Streeting’s allies, meanwhile, say that while the former health secretary has earned a reputation as a Blairite moderniser who believes in private sector provision of public services, he is also supportive of Burnham’s deprivatisation agenda.

Sources close to the former health secretary said he had “struggled to find differences of opinion” with Burnham over economic policies, believed privatisation had been a failure and agreed with the Makerfield MP that Thames Water should be nationalised.