Dame Helen Ghosh, the conservation trust's director-general, told The Times it would make up its mind about the controversial gas extraction procedure after seeing the evidence on its environmental impact.
It appears to be a move away from the trust's previous stance of a "presumption against fracking" on its land "because natural gas is a fossil gas", a position it held during the anti-fracking protests in August when the firm Cuadrilla drilled a test well at Balcombe in West Sussex.
Dame Helen said the trust was worried that fracking might "perpetuate a reliance on fossil fuels", but said that gas was "less bad" than coal in terms of carbon dioxide emissions.
She added: "I'm not saying we will never allow fracking on our land.
"We all have yet to see what the surface environmental impact of fracking is and when we have seen it then we would reach a view about whether (we would object to it) adjacent to National Trust land or on National Trust land.
"We are waiting for the evidence. We have an open mind."
Dame Helen also said it was unlikely that the National Trust "would ever promote or allow a wind farm on our land", but would not say whether this was because of the visual intrusion of wind farms.
And she admitted that the trust was well behind on its own targets for reducing reliance on fossil fuels and for conserving energy.
More than 100 people were arrested during protests against Cuadrilla's test drilling, including former Green Party leader and Brighton Pavilion MP Caroline Lucas.
Opponents of fracking, in which water and chemicals are pumped into the ground at high pressure to fracture shale rock and release gas, fear it could harm water resources and cause small earthquakes, and development of the sites will cause noise and traffic.