It marks the latest attempt by the pair to join forces after a proposed deal collapsed in 2000, and then again in 2004-5.
Shares in FTSE 100-listed LSE jumped as much as 17% after it confirmed "detailed discussions" over a possible all-share merger.
The LSE said it would be a "merger of equals", forming an enlarged group that would rival the likes of CME Group and Intercontinental Exchange in the US and Hong Kong Exchanges and Clearing, which is the world's largest exchanges group.
Latest talks between the two come nearly 16 years after LSE and Deutsche Boerse first sought to strike a deal.
The LSE said it is working on plans that would see LSE shareholders hold 45.6% of the combined group and Deutsche Boerse the remaining 54.4%.
All key businesses of LSE and Deutsche Boerse would continue under their current brand names and it would have a single board made up of an equal number of directors from the two firms.
The LSE said discussions remain ongoing over the other terms and conditions of the deal.
"The potential merger would represent a compelling opportunity for both companies to strengthen each other in an industry-defining combination, creating a leading European-based global markets infrastructure group," the LSE said.
It added that "complementary growth strategies, products, services and geographic footprint" would allow the enlarged group to offer a "full service offering to customers on a global basis."
The London Stock Exchange is one of the world's oldest stock exchanges and can trace its history back more than 300 years.
The wider LSE Group was formed in October 2007 when the London Stock Exchange merged with Milan stock exchange Borsa Italiana.
It has completed a series of deals since then, the biggest of which was its £1.6bn takeover of American stock index and asset management business Frank Russell in 2014.
Other deals include buying out the remaining 50% of FTSE International it did not already own in 2011, followed by a majority stake in clearing house LCH.Clearnet Group in March 2013.
Deutsche Boerse is listed on the Dax in Germany, having listed on the stock exchange in February 2001.