The offer would apply only to Hong Kongers who possess a document known as the British National Overseas (BNO) passport, which was granted to residents who registered for it prior to Britain handing Hong Kong back to China in 1997.
On Thursday, Britain's Home Office Secretary, Priti Patel, said she and the Foreign Secretary Dominic Raab were exploring ways to provide more rights for BNO passport holders, including extending a "path to citizenship."
It followed an announcement by Raab earlier on Thursday in which he told the British press that greater visa rights were in the cards for BNO passport holders.
"In relation to BNO passport holders, as you know, currently they only have the right to come to the UK for six months. If China continues down this path and implements this national security legislation, we will change that status," he said.
"We will remove that six-month limit and allow those BNO passport holders to come to the UK and to apply to work and study for extendable periods of 12 months and that will itself provide a pathway to future citizenship," he added.
Widespread condemnation
China's proposed national security law has been met with protests in Hong Kong and criticism internationally. Observers warn that it could curtail many of the fundamental civil liberties guaranteed in the transition from British to Chinese rule.
Once the law has been drafted, it will implemented upon promulgation by the Hong Kong government, bypassing the city's legislature via a rarely-enacted constitutional backdoor.
China's move to assert greater control in Hong Kong has also mounted tensions between Beijing and Washington. Following protests in the city Wednesday in which around 300 people were arrested, US Secretary of State Mike Pompeo denounced the law as a "disastrous decision" and "the latest in a series of actions that fundamentally undermine Hong Kong's autonomy and freedoms."
He added that the country would no longer consider the global financial hub as autonomous from China for trade and economic purposes.
CNN's Nectar Gan contributed to this report.