Hong Kong Exchanges and Clearing (HKEX) said it was yet to make a firm offer but its plans would create a "global market infrastructure leader".
The terms of its cash and shares proposal would value the London Stock Exchange Group (LSEG) at £8.36 per share, or £29.6bn.
Shares in LSEG were trading 16% up in the moments after the announcement was made but later settled 10% higher at £6.60 per share. They closed up nearly 6% on the day at £7.20.
The company had a market value just shy of £24bn at the start of the day's trading.
The Hong Kong exchange said a deal would provide the LSE with a key opening to Asian markets and underpin London's role as a key financial hub - currently seen as potentially threatened by Brexit.
Hong Kong itself has seen its own hub status threatened by civil unrest over Chinese rule.
HKEX said it would also seek a secondary listing in London on the completion of a merger.
The firm's statement said: "The proposed combination would strengthen both businesses, better position them to innovate across markets and geographies, and offer market participants and investors unprecedented global market connectivity."
The company is required, under City rules, to make a firm offer by 9 October.
The Hong Kong firm made its push following failed attempts by the LSEG to join forces with rivals, including three involving Deutsche Boerse, though the latest merger was plan blocked by the EU in 2017.
LSEG revealed last month it was in talks to buy Refinitiv, the financial data provider, for $27bn (£21.6bn) and HKEX made it clear that the purchase was not part of its plans.
LSEG said in response: "HKEX has made an unsolicited, preliminary and highly conditional proposal to acquire the entire share capital of LSEG.
"The board of LSEG will consider this proposal and will make a further announcement in due course.
"LSEG remains committed to and continues to make good progress on its proposed acquisition of Refinitiv Holdings Ltd as announced on 1 August 2019.
"A circular is expected to be posted to LSEG shareholders in November 2019 to seek their approval of the transaction."
The proposal comes hot on the heels of a takeover by Hong Kong's wealthiest man, Li Ka-shing, of the UK pub owner and brewery group, Greene King.
The takeover deal - and wider merger and acquisition activity involving UK firms - has been attributed to the weakness of the pound as investors fret over the prospect of a no-deal Brexit as it makes UK shares cheaper for foreign buyers.
Commenting on the swoop Richard Hunter, head of markets at interactive investor, said the complementary strengths of the two exchanges would make strategic sense.
He wrote: "Part of the proposal requires that the Stock Exchange back away from its recent $27bn deal to acquire Refinitiv, which appears to be an early stumbling block."
He added: "The proposal is a fascinating prospect, but far from a done deal.
"The fact that the LSE share price has already retreated from the initial 10% spike on release of the news may reflect some initial scepticism around the likelihood of the deal going through."