Lam had suspended the bill in June and later said that it was "dead", but demonstrators have always been suspicious of her government's refusal to formally withdraw the bill and feared it could be revived at a later date.
The Hang Seng index leapt more than three percent in afternoon trade after the South China Morning Post and HK01 both published reports that the city's pro-Beijing chief executive Carrie Lam was planning to shelve the bill.
The Hong Kong stock market soared 4%, boosted by the possible bill withdrawal.
Fellow pro-democracy activist Nathan Law told the BBC that their campaign would go on. These include a formal withdrawal of the extradition bill, an inquiry into police handling of the protests and the release of arrested protesters.
Videos showing the man being apprehended by the police in the station have been widely shared on social media with protest groups and activists saying it is evidence of police brutality. "We deserve to elect our own government".
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Beijing has said it would retaliate by targeting $75 billion in United States goods, beginning in part on September 1. O'Rourke's plan would wipe out Trump's tariffs against China in exchange for Beijing ending tariffs on USA imports.
Gregori Volokhine, fund manager at Meeschaert Financial Services, said Lam's decision in Hong Kong "removed a big worry" for investors who had feared a muscular response from Beijing to the demonstrations.
While Lam has promised police tactics will be reviewed, she said it will occur under the Independent Police Complaints Council, a body within the Hong Kong Police Force - as opposed to an independent inquiry.
Pro-democracy lawmaker Au Nok-hin took to his Facebook page and wrote: "Five demands, not one less".
Lam also added that she would like to set up public dialogue, liaising with community leaders and academics.
After that, "appropriate assistance" will be given if necessary, the statement said, noting that so far, the government has never sent any asylum seeker to a country or area where he or she could be tortured or treated inhumanely. Lam has tweaked the proposals but has refused to withdraw the bill, saying it is vital to plug a long-standing "loophole".
"I hope the people in China can understand that democracy, freedom and human rights are universal values that Hong Kong people are fighting for", he told journalists before a forum in Taipei, Taiwan, where he is visiting.
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The US has provided Chinese authorities with only six tips relating to illegal fentanyl smuggling in China since 2012, said Liu. Consequently China is preparing to defend its legal rights in compliance to the rules of the WTO.
Police have arrested more than 1,100 people since the protests started.
"It is too little, too late".
Another pro-establishment lawmaker, Felix Chung, said that withdrawing the bill would "certainly" help.
For much of the last three months Lam has struck a defiant tone, appearing either unwilling or unable to make any concessions.
According to a leaked audio recording, Lam said she now has "very limited" room to resolve the crisis because the unrest has become a national security and sovereignty issue for China.
June 6 - More than 3,000 Hong Kong lawyers take to the streets dressed in black in a rare protest march against the extradition law. Instead, she named two new members to a police watchdog agency investigating the matter.
China asserts authority to declare state of emergency in Hong Kong
Lam said on Tuesday that her government had the confidence of Beijing and could bring an end to unrest itself. "I have not even contemplated discussing resignation with the central people's government".
"I know it is not going to be an easy path, and that's why I have said that I have not given myself the choice to take an easier path and that is to leave".