Rachel Reeves has insisted she has “unfinished business” as chancellor as she pitches herself for a role in Andy Burnham’s new cabinet.The chancellor has found herself at the centre of rumours that she could be ousted or demoted from her role if, as expected, the Makerfield MP becomes the next prime minister.As she fights to remain in her current role, Ms Reeves said on Thursday she is “backing” Mr Burnham to be the next prime minister, but said she could not “pre-empt” his decision.Speaking at the British Chambers of Commerce conference in central London on Thursday, Ms Reeves was asked if she wanted to stay on as Mr Burnham’s chancellor.Rachel Reeves has insisted she has “unfinished business” as chancellor as she pitches herself for a role in Andy Burnham’s new cabinet (Getty)She replied: “Those would be choices for him. I’m not going to pre-empt those, when he becomes prime minister he will make those decisions around the top team around him, but I’m not going to pre-empt those decisions.”Asked if she had “unfinished business” in the role, she said: “I’m really proud of my record and I think in those two years, if you look at, first of all, those key macro-numbers on inflation, on interest rates, on economic growth, the fact that wages have risen faster than inflation for every single month that I’ve been chancellor of the exchequer.”She also said fiscal devolution - an issue at the heart of Andy Burnham’s priorities - was one area there is “certainly unfinished business”.Mr Burnham is yet to settle on his new chancellor, but Ms Reeves earlier would not be drawn on reports she may accept another role in his cabinet.Speculation has so far focused on the energy secretary Ed Miliband or former health secretary Wes Streeting, who said he would not stand against Mr Burnham despite earlier insisting he would run in a future Labour leadership contest.Mr Burnham is yet to settle on his new chancellor, but Ms Reeves earlier would not be drawn on reports she may accept another role in his Cabinet (PA)But some within Labour have cautioned against appointing Mr Miliband, with chief secretary to the prime minister Darren Jones appearing to suggest the former party leader would not meet his “tests” for a new chancellor.Mr Jones said any new chancellor should not seek to “control” the prime minister, and would have to “reassure” markets, trade unions, MPs and the public – and he declined to say whether he thought Mr Miliband passed those “tests”.Ms Reeves also urged her successor to stick to her economic plans, which she insisted were “beginning to bear fruit”, while she praised Mr Burnham for committing to her fiscal rules.“I think that Andy Burnham, who will be the next prime minister, has been really clear that he is committed to those rules,” she said.Andy Burnham returned to the House of Commons to take up his seat after winning the Makerfield by-election (PA) (PA Wire)“And that is a good thing, because it means that businesses here can be confident that that stability… which is essential for getting inflation and interest rates down, will be continued.”She added: “I hope that whoever is chancellor in the future, whenever that future may be, sticks to what I’m doing because it is beginning to bear fruit, and we are seeing that investment return to the economy, that growth return to the economy, and crucially, that stability, so that businesses can plan and invest in the future.”Sir Keir Starmer has signalled he is squarely focused on tackling the cost of living and remaining professional, despite turmoil at the top of government.The prime minister said on Thursday he hoped to ensure disruption was “absolutely minimised” as he hands over power following his final weeks in Downing Street, as it appears Andy Burnham is likely to succeed him without a Labour leadership contest.Mr Jones had been rumoured as a potential challenger backed by Sir Keir’s supporters among Labour MPs, but on Wednesday he ruled himself out of contention and rowed in behind Mr Burnham.Sir Keir Starmer has signalled he is squarely focused on tackling the cost of living and remaining professional, despite turmoil at the top of governmentSpeaking in the Commons on Thursday morning Mr Jones referenced his future, as he said he was “starting to prepare (himself) for a quieter life”.He later said he was hoping to return to the despatch box “in due course”.Former armed forces minister Al Carns, who resigned earlier this month in a row over defence spending, remains a possible contender, calling for a “proper debate” on the country’s future.While Mr Carns has not formally announced a leadership bid, he has also refused to rule himself out as a potential candidate in a series of interviews in recent days.