The exchange made a hostile bid for its London counterpart in 2000.
Already the subject of bids from Deutsche Bourse and Euronext NV, a number of newspapers reported a further approach from Australia’s Macquarie Bank.
The Business cited a source close the LSE as describing any move by Macquarie as a “non-starter”, adding they would have to bid more than £1.5 billion to have any chance.
According to The Sunday Telegraph the Australian bank approached LSE two months ago, and is pressing ahead with the bid.
The battle to control the LSE began in December last year, when Deutsche Boerse tabled an informal offer of 530 pence per share, valuing the group at £1.3 billion.
The offer was later rejected as too low.
Deutsche Boerse has since shelved its takeover attempt in response to pressure from its own shareholders, but has reserved the right to renew its bid if Euronext tables a firm offer, or if another bidder emerges.
Euronext has also expressed its interest, but has not said how much it is prepared to pay.