The company said it had been trying for almost a year to get permission for a seismic survey at Clumber Park in Nottinghamshire.
Ineos said it has repeatedly tried to arrange a meeting, adding that the Trust refuses to speak to the company.
“If the National Trust refuses to change its position, Ineos will have no choice but to write to the Oil and Gas Authority, asking for permission to seek a court order enforcing its rights to carry out these surveys on National Trust land,” said a statement.
Corporate affairs director Tom Crotty told the Press Association the process would be “totally non evasive”, with virtually all the work done overground.
The East Midlands is a key area for potential shale gas extraction and Ineos already has permission from landowners around the Trust's park, he said.
The ability of Ineos to extract shale gas would be “significantly limited” if tests could not be carried out on the Trust's land, said Mr Crotty.
Ineos will decide its next move within weeks, depending on the Trust's response to a letter it received on Thursday.
Mr Crotty said Ineos needed to carry out the survey to get a full picture of the potential for shale gas extraction in the area.
Ineos said Government licences give the company a legal obligation to investigate shale gas deposits in areas around the country, including Clumber Park.
“The geological surveys are classed as non-intrusive. They involve the use of specialist trucks to create and record sound waves in order to map rocks deep underground.
“The condition of the land is recorded before the survey and restored to the same condition afterwards.
“Ineos has agreed to share the results with the national archives for the benefit of the nation and future generations. Hundreds of other landowners have already agreed to the surveys,” said a statement.
Lynn Calder, commercial director of Ineos Shale, said: “The National Trust is taking an overtly political position against all fossil fuels.
“What it fails to recognise is that shale gas is 50% cleaner than coal and 30% cleaner than oil. The development of shale gas will actually reduce greenhouse gas emissions.
“We are developing a shale gas industry that is safe and essential for the UK and the economy. It is estimated that the industry will create tens of thousands of well-paid jobs and Ineos has pledged to give 6% of revenue to local people - potentially amounting to billions of pounds.”
Ineos has asked the National Trust to respond to its letter and agree to the surveys.
If that cannot be achieved the company will “reluctantly” have to pursue legal action.
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