The Qatar Investment Authority has bid $5.62 billion for U.S exchange Nasdaq's stake in the British bourse, according to unnamed sources cited by the British newspaper the Sunday Times.
The price equates to around 1,400 cents per share.
It is thought that Nasdaq, which has previously indicated it would like to complete the disposal by September, is seeking the sale to fund its approach for its latest target Nordic exchange operators OMX.
The US exchange bought the stake in LSE last year as part of its unsuccessful bid to acquire the UK bourse operator.
Should the deal for LSE go through, it would represent the latest investment approach to UK companies from the Middle East, following Qatar Investment Authority's offer to buy supermarket giant J Sainsbury and the successful acquisition of cruise company P&O by Dubai's state-owned Ports World.