Shares in the LSE soared 17% after it said it was in "detailed discussions" with the German company about a "merger of equals".
Both companies said all their key businesses would continue to operate under their current brand names.
It is the third time the LSE and Deutsche Boerse have tried to strike a deal, first in 2000 then in 2004-5.
Shares in Deutsche Boerse rose 7%.
Under the terms of a potential deal, the LSE would own 45.6% of the merged group and Deutsche Boerse would hold the remaining 54.4%.
The combined business would have a single board, made up of an equal number of directors from the two companies.
Markus Huber, an analyst at stockbroker City of London Markets, said: "Although negotiations seem to be at a very early stage, a tie-up would  make sense in regard to possibly synergies and overall improvement of  competitiveness versus their main rivals."
In a statement, the LSE said: "The boards believe that 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."
In 2000, the LSE and Deutsche Boerse announced they were in merger talks. However, the LSE was forced to pull out of discussions when the deal was gatecrashed by Sweden's OM Exchange which made a Â£808m hostile bid for the British business. The LSE rejected the offer.
In December 2004, Deutsche Boerse made a Â£1.3bn approach for the LSE but saw its offer rebuffed.
London Stock Exchange (LSE) has confirmed merger talks with Germany's Deutsche Boerse.