The Government wants to hand over a quarter of woodland to new or existing trusts.
A further quarter will be offered to communities and charities, with the rest being put on the open market.
The move will see 258,000 hectares managed by the Forestry Commission sold to private bidders.
More than 288,000 people have signed a petition to halt the sale.
National Trust director Dame Fiona Reynolds said:
"This is a watershed moment in the history of the nation. These much-cherished places have been in public hands for centuries, enjoyed by everyone for generation after generation.
"For 116 years, the National Trust has helped to save the places the people of this country most value when their existence, or access to them, has been threatened.
"If the Government is determined to pursue the course of action it has outlined and the public wish us to, we are ready to play our part in giving them a secure future. We are ready to step in."
The trust will conduct a consultation before putting proposals to its board of trustees in three months.