Ineos wants to conduct seismic surveys at Clumber Park in Nottinghamshire to see if there is potential for fracking.
The firm said the charity had blocked any contact for almost a year and it was considering seeking a court order.
The National Trust said it opposed any activities leading to the extraction of fossil fuels, so rejected requests.
Moves to look for shale gas in the Sherwood Forest area have proved controversial due to environmental concerns over extraction - known as fracking - and expansion of fossil fuel use.
Ineos said it already had permission from nearby landowners for the the non-invasive survey and its ability to extract gas would be "significantly limited" if it could not get on to Clumber Park.
"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," it said in a statement.
The company said government licences gave it a legal obligation to investigate shale gas deposits around the country and criticised the charity's position as "overtly political" as shale gas had lower carbon emissions than either oil and gas.
A National Trust spokesman said: "The National Trust is opposed to fracking on its land and will reject any fracking requests or inquiries.
"Consistent with this, we say no to surveying on our land for fracking purposes."

Kirsty Blackman, SNP MP for Aberdeen North, found a toy rabbit at the Carriage Gates entrance last July.
She tried to trace the owner on social media but no-one came forward for months.
After turning to Mumsnet, a user got in touch at Hogmanay, saying the toy belonged to her six-year-old daughter.
The woman said she worked near Westminster at the time and her daughter was "gutted" when the bunny went missing as they had been "inseparable since birth".
She reclaimed the toy on a visit to the House of Commons on Wednesday.
Ms Blackman updated followers on the toy's time at Westminster, including pictures of her and the Jellycat Bashful Bunny with Big Ben behind them and at Prime Minister's Questions.
She also drafted an Early Day Motion stating the House of Commons is "saddened by the discovery of the abandoned bashful bunny by the gates of the Palace of Westminster" which was not submitted to parliament but was signed by several SNP colleagues.
Ms Blackman said previously: "I have two young children, so I know the devastation that can be caused when a toy is lost."

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5 February 2014 Last updated at 08:46 GMT
White lions are very rare - their zoo keeper thinks there's only around 90 of them in existence.
They are usually found in wildlife reserves in South Africa and a few zoos around the world.
Check out the clip and see the newborns settling in...
A petrochemical company is threatening legal action over the National Trust's refusal to allow testing for shale gas on its land.
[NEXT_CONCEPT]
An MP who issued a social medial appeal after discovering a soft toy abandoned outside the House of Commons has reunited it with its young owner.
[NEXT_CONCEPT]
Three white lion cubs have been born at a zoo in Poland, in eastern Europe.