An agreement to pay compensation could have broad implications for thousands of people who say they were abused by authorities in Britain's former colonies.
Law firm Leigh Day, which represents three elderly Kenyans seeking compensation, confirmed talks were taking place, but gave no other details, "due to the nature of the negotiations."
The Foreign Office declined to comment on an ongoing legal case.
The case involves Kenyans who say they were beaten and sexually assaulted by officers acting for the British administration trying to suppress the "Mau Mau" rebellion, in which groups of Kenyans attacked British officials and white farmers who had settled in some of Kenya's most fertile lands.
In 1952, then-Prime Minister Winston Churchill declared a state of emergency in the country and sent British and African soldiers to help colonial administrators capture the fighters and send them to detention camps.
Thousands of Kenyans were detained, including U.S. President Barack Obama's grandfather, Hussein Onyango Obama.
In October, Britain's High Court ruled that three Kenyans—Wambugu Wa Nyingi, Paulo Muoka Nzili and Jane Muthoni Mara—could pursue claims for compensation.
The government had sought to have the case dismissed, saying it could not be held legally responsible for long-ago abuses. It argued that the liabilities of the colonial administration passed to the Kenyan government when the country gained independence from Britain in 1963.
The government launched an appeal against the October ruling, although it did not dispute "that each of the claimants in this case suffered torture and other ill treatment at the hands of the colonial administration."
The Guardian newspaper reported Monday that an appeals hearing had been put on hold while negotiations were held.
While not commenting directly on the case, the Foreign Office said in a statement that "it is an enduring feature of our democracy that we are willing to learn from our history."
"Our relationship with Kenya and its people has moved on and is characterized by close co-operation and partnership, building on the many positives from our shared history," it said.
Agreement of compensation could bring payouts to thousands of Kenyans who allege similar abuse, and also could trigger claims from other former British colonies.