Mr Balls, accused in the book of being part of a parallel Treasury operation within the last government, was considered as a replacement for Mr Darling in 2009 by Gordon Brown.
In a sign that Labour expected the Conservatives to seize on the account, Mr Balls acknowledged there was "nothing better" for George Osborne than the possibility of revisiting the past.
Extracts from Mr Darling's Back From The Brink: 1,000 Days At No 11 have appeared on the Labour Uncut website and the book is set to be serialised in a newspaper at the weekend.
The website claims Mr Darling identifies Mr Balls and former business minister Baroness Vadera, key allies of former prime minister Mr Brown, as running an alternative Treasury unit.
Mr Darling also confirms that Mr Brown tried to force him out of No 11 in 2009.
Mr Balls told BBC Radio 4's World at One that Mr Brown did not tell him what he planned and insisted that he made clear he wanted to stay in his job as children's secretary.
He said: "I thought Alistair did a good job as chancellor in very difficult periods."
Asked about Mr Brown's plan, Mr Balls said: "He never told me that was what he was doing, but there's no doubt from what Alistair's saying and what everybody else has said, and the conversations that happened in that week, that that was the plan.
"I made it clear in that week to people in government and outside I thought that was the wrong plan.
"I thought changing the chancellor in 2009 was the wrong decision and I wanted to stay in the department as Secretary of State for Children, Schools and Families."
He said the issue was "history" but in a sign that the party recognised the potential damage the memoir could cause, Mr Balls said: "I have to say that if I were George Osborne at the moment, totally on the defensive on my failing economic plans, I would think there's nothing better than a book, a memoir, some revisiting of the past.
"The world's moved on. There's big challenges today, that's my job.
"Look, people want to write their memoirs and that's fine, but let's focus on the jobs and living standards of families for the future, that's what really matters for our country."
Mr Balls told Sky News: "Any disagreement I had with Alistair I had with him to his face.
"We didn't agree about VAT, that's clear and on the record, and I think Alistair did a great job during that time."
Labour leader Ed Miliband told Sky News he was concentrating on the issues facing the country now.
He said: "Alistair's got a perfect right to write his memoirs and talk about his reflections on his time in office, and I'm sure they will be interesting for people.
"But the important thing for me to do, which I'm going to do, is talk about the needs of the economy going forward and the needs of the country."
In the latest extracts reported on Labour Uncut, Mr Darling was scathing about some of the senior figures at banks at the time of the crash, claiming former RBS chief executive Sir Fred Goodwin "deserved to be a pariah" for refusing to give up his pension after taking the lender to the brink of collapse.
He described Sir Fred's attitude to the crisis as in keeping with someone "off to play a game of golf".
Mr Darling described former HBOS chief executive Andy Hornby as "looking like he was about to explode" when faced with the scale of what had occurred.
The former chancellor said: "My worry is that they (the bankers) were so arrogant and stupid they might bring us all down."
The book is also set to give an insight into former prime minister Gordon Brown's "brutal and volcanic" demeanour.
Publisher Atlantic Books refused to comment on the Labour Uncut story.
Speaking in Glasgow today, Mr Brown said he was not going to "get into politics" when asked if he had a response to the comments attributed to Mr Darling.
Asked about his reaction to the description he had a "brutal and volcanic" demeanour, the Labour MP for Kirkcaldy and Cowdenbeath said: "I'm here to talk about football and I'm talking about the sport I love, I've always followed, and I'm not going to get into politics today."
He was speaking at a press conference at the Scottish Football Museum Hall of Fame at Hampden Park stadium in the city.
Mr Brown was announced as the new patron of the John Thomson Memorial Committee, to mark the 80th anniversary of the Celtic and Scotland goalkeeper's death.
He continued: "I'm here to talk about football and that's what I'm going to talk about today.
"I think the memory of John Thomson deserves better than us answering questions on other things today."
PA
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