The Prime Minister will announce plans to permanently drop the commitment to give MPs a free vote on whether to overturn the fox hunting ban in early 2018, the Sunday Times reports.
Going ahead with the U-turn risks infuriating Tories in rural parts of the country.
The plans were described as "pure speculation" by a Downing Street source.
They added: "There is no vote that could change the current policy on fox hunting scheduled in this session of Parliament."
Since Michael Gove was appointed as environment secretary by Mrs May after the June election, he has placed animal welfare at the top of his priority list.
During the election campaign Labour leader Jeremy Corbyn criticised Mrs May for saying she was in favour of fox hunting, which crushed the prime minister's authority after the Conservatives lost their Commons majority.
During a visit to a Leeds factory during the election, Mrs May said: "As it happens, personally, I've always been in favour of fox hunting and we maintain our commitment - we had a commitment previously - as a Conservative Party to allow a free vote and that would allow Parliament to take a decision on this."