Environment Secretary Caroline Spelman will address MPs at about 1300 GMT, and is expected to confirm the current consultation is being halted. Instead, it is understood a new panel of experts will be set up to look at public access and biodiversity within the publicly owned woodland.
Labour said it showed the government was "incompetent" and "out of touch".
David Cameron hinted on Wednesday that he was backing away from the policy. Asked during Prime Minister's Questions whether he was happy with the plans, he said no.
Another government source said the Public Bodies Bill, which allows for woodlands to be sold off, would now be amended. "We have heard enough from the consultation to know what to do," the source told the BBC.
The proposals to offload 258,000 hectares run by the Forestry Commission have attracted cross-party criticism and a public outcry, with Labour accusing ministers of "environmental vandalism". The plans were intended to give the private sector, community and charitable groups greater involvement in woodlands by encouraging a "mixed model" of ownership.
But critics argued it could threaten public access, biodiversity and result in forests being used for unsuitable purposes. The public outcry over the plans led to half a million people reportedly signing a petition against the sell-off.
BBC Radio 4's chief political correspondent Norman Smith said: "Mr Cameron has decided, yes, it's painful to carry out a U-turn, but better that and one day's bad headlines, than months of wrestling with Middle England."
Labour leader Ed Miliband MP said: "Virtually every person in the country could see selling off our forests was a foolish and short-sighted policy but they went ahead regardless. Now they are panicked into a retreat hours after Mr Cameron said they would carry on with their consultation. This is a chaotic and incompetent way to run government."
He added: "Just as people are angry about the threat to the forests, so too the threat to local libraries, children's centres, other common institutions."
The government is allowed to sell off 15% of England's woodlands in each four-year public spending period. The current planned 15% sale is on hold while criteria are examined to ensure public benefits are protected, ministers say, but it is due to go ahead over the next four years - raising an estimated £100m.
Ms Creagh also expressed concern over job cuts due at the Forestry Commission, which will see it lose a quarter of its workforce. "Over 400 foresters are going to be made redundant, and we really have to ask the government how can they protect access and promote biodiversity when they're losing the very people who do that job on the ground," Ms Creagh said.