A settlement that could reach £600,000 has been agreed, though Ms Shoesmith may receive a lower sum, according to BBC2's Newsnight. Some of the cash will come from central government coffers but Haringey council, in north London, will foot most of the bill, it reported.
Mr Balls removed Ms Shoesmith from her £133,000-a-year post as Haringey Council's director of children's services after a damning report on the death of Peter Connolly.
She was then fired by the council without compensation in December 2008, after a report from regulator Ofsted said her department failed to protect 17-month-old Peter, then known publicly as Baby P. She has reportedly not worked since.
Mr Balls, now shadow chancellor, told BBC Radio 5 Live: "An independent report said there were disastrous failings in Haringey children's services. Sharon Shoesmith was the director of children's services and so of course it leaves a bad taste in the mouth that the person who was leading that department and responsible, ends up walking away with, it seems, a large amount of money."
Downing Street said the Department for Education's contribution to the payout would be made public.
The settlement was condemned by Communities and Local Government Secretary Eric Pickles, who said Haringey Council was "bankrolling a state-sponsored cover-up".
He said: "There should be no rewards for failure in the public sector or the private sector.
"We've been very clear that legal devices like non-disclosure or compromise agreements should not be used to gag staff or brush under the carpet golden goodbyes to senior staff.
"I fail to see how Haringey Council's secretive actions are in the public interest, given the astonishing sum of taxpayers' money involved and the immense public concern and upset at the Baby P scandal."