Cabinet ministers loyal to Keir Starmer have said they will not back any candidate against Andy Burnham, urging the chief secretary to the prime minister not to run in a contest.

Darren Jones is being urged by some MPs to run against Burnham to avoid a “coronation” of the former Greater Manchester mayor, though several backbenchers tentatively backing Jones said they were doing so to put the spotlight on Burnham’s economic policies and to warn of the prospect of Ed Miliband as chancellor.

Jones, the MP for Bristol North West, is understood to be reluctant to run, but sources said he would look at Burnham’s economic plans, including for public control of utilities, before deciding.

Supporters of Jones said they had concerns about the possibility of Miliband becoming chancellor because it could cause a negative market reaction. “Ed as chancellor would be a disaster,” one said. “Many members know that.”

Several cabinet ministers said, however, that they did not think there should be another candidate to challenge Burnham. Two senior ministers who have been loyal to Starmer have already got behind Burnham: the Scottish secretary, Douglas Alexander, and the Cabinet Office minister Nick Thomas-Symonds.

Another said: “It would be crackers to have a contest at this stage. We have to move on from this period and try to pull together.” One minister said they had urged Jones not to run in any contest where he would be unlikely to win.

Burnham is considering appointing Miliband as chancellor but has not made a final decision. Sources said Burnham was aware of the potential risks, with business and unions opposed to the move, but could be prepared to make the argument about why a bolder approach was needed.

The new Makerfield MP, who is the strong favourite to become leader and prime minister, is understood to be planning a series of speeches to set out his policies, including on the economy. He has stressed that he will stick to Rachel Reeves’s fiscal rules on spending and debt.

MPs have been organising for a potential run for Jones – who is also the chancellor of the duchy of Lancaster – since last Friday in case Starmer resigned. One said they were considering backing an alternative candidate because of the backlash they were receiving from party members about giving them no say in who led the party.

One MP backing Jones said: “Many in the party know that Andy Burnham’s policies are at best the same policies that we put to the electorate in 2010, 2015, 2017 and 2019. Every time, the electorate rejected them.

“Unlike all other potential candidates, Darren Jones has both the economic and national security experience we would expect from a PM and represents continuity in both those successful areas. But he also represents a generational break from most other candidates, has national rather than regional appeal, and is a proven media performer.”

But most MPs said they believed Jones had no chance of reaching the threshold of 81 MPs’ support to enter the contest, with one saying the numbers were “barely in double figures”.

The former defence minister Al Carns has also been considering a run for leader. “I’m not ready to make a decision on this in any way shape or form,” the former Royal Marine said. “What I would say is we need to move from the politics which talk through the tactics and actually think about the strategy, and what I’m really looking for are big-objective outcomes that we want to get to in 2029 and 2034-35.”

Thomas-Symonds told BBC Radio 4’s Today programme on Tuesday he did not think a contest was in the interests of the country. Burnham is said to have up to 300 MPs backing his bid to replace Starmer.

Asked if that meant he wanted to avoid a contest, Thomas-Symonds said: “I just think we have to weigh up what is in the best interests of the country. I am of the view that it needs to be a swift transition, but of course I understand colleagues have difficult decisions to make.

“I am backing Andy Burnham to succeed Keir. I think, first of all, we have a job of delivery to do in the second half of the parliament. I think he has shown, Andy, comprehensively as the mayor of Greater Manchester, that he can carry out that job of delivery.

“But secondly, there is the question about leading us into the next general election and defeating Reform and I think Andy Burnham has just shown comprehensively in Makerfield that he can do that, we’ve seen him do it in an election.”