Chinese billionaire Jack Ma’s financial technology firm,Ant, is aiming to raise more than $34bn (£26.15bn) .
Advisers to Ant set the share price on Monday amid reports of very strong demand from major investors.
The previous largest debut was Saudi Aramco's $29.4bn float last December.
The company, which has bypassed US markets, confirmed that it is splitting its shares equally between the Shanghai and Hong Kong stock markets and is seeking to raise about $17.2bn in each city.
Ant, an online payments business, is only selling about 11% of its shares. But the pricing values the whole business at about $313bn.
Ant runs Alipay, the dominant online payment system in China, where cash, cheques and credit cards have long been eclipsed by e-payment devices and apps.
The snub of US markets, which are already overloaded with tech giants from Google and Facebook to Apple and Amazon, is a coup for Asia’s financial centres and comes amid rising political and trade tensions between Beijing and Washington.
Trump is in the process of attempting to force the hugely popular video sharing site TikTok,to sell its US operation to an American owner or face being shut down. He claims it is a potential threat to national security as the Chinese government could gain access to user data, an accusation that TikTok’s parent company denies.
The Trump administration has threatened to limit Chinese firms' access to US capital markets.In response, China called on its flagship tech giants to list on domestic stock markets.
Chinese tech firms, including NetEase and JD.Com, have already raised billions by selling their shares via the Hong Kong stock market.
Ant, which is on track to raise more than the $25bn its former parent Alibaba Group managed in flotation in 2014, is expected to start trading on 5 November on Hong Kong’s technology-focused Star market. The company has not disclosed when its shares will begin trading in Shanghai.
Ant is selling 3.34bn shares in the flotation, accounting for 11% of the group’s total outstanding stock.
Mr Ma told a conference in China on Saturday that the flotation would be of huge significance for Shanghai and Hong Kong.
"This was the first time such a big listing, the largest in human history, was priced outside New York City," he told the Bund Summit.
"We wouldn't have dared to think about it five years, or even three years ago," said Mr Ma.
Major investors to have signed up to the share offering ahead of flotation, scheduled for 5 November, include Singapore state investor Temasek Holding and Abu Dhabi sovereign wealth funds GIC and Abu Dhabi Investment Authority.