Foreign Secretary Dominic Raab, who on Sunday accused China of gross human rights violations, will announce the suspension of the treaty in parliament, the Times and Daily Telegraph newspapers said, citing sources.
Prime Minister Boris Johnson said changes would be announced later on Monday to reflect concerns over the security law, but did not specify what those changes would be.
"We've got to have a calibrated response and we're going to be tough on some things, but also are going to continue to engage," Johnson told reporters.
Raab is due to speak in parliament at 1430 GMT.
In Beijing, asked about the reported suspension of extradition arrangements, Chinese foreign ministry spokesman Wang Wenbin urged Britain to "stop going further down the wrong path".
Any move on extradition would be another nail in the coffin of what then Prime Minister David Cameron in 2015 cast as a "golden era" of ties with China, the world's second-largest economy.
But London has been dismayed by a crackdown in Hong Kong, which returned to Chinese rule in 1997, and the perception that China did not tell the whole truth over the coronavirus outbreak.
Last week Prime Minister Boris Johnson ordered Huawei Technologies equipment to be purged completely from Britain's 5G network by the end of 2027.
China has accused Britain of pandering to the United States.
Britain says the new security law breaches the guarantees of freedoms, including an independent judiciary, that have helped keep Hong Kong one of the world's most important trade and financial centres since 1997.
Hong Kong and Beijing officials have said the law is vital to plug holes in national security defences exposed by recent pro-democracy and anti-China protests. China has repeatedly told Western powers to stop meddling in Hong Kong's affairs.
On Sunday, the Chinese ambassador to Britain warned of a tough response if London attempted to sanction any of its officials, as some Conservative Party lawmakers have demanded.
"If UK government goes that far to impose sanctions on any individual in China, China will certainly make a resolute response to it," Liu Xiaoming told the BBC's Andrew Marr Show.
Raab told the same programme he would not be drawn on future additions to Britain's sanctions list but he denied that Britain would be too weak to challenge China through this channel.
