The potential sale would allow LSE to "address proactively anti-trust concerns raised by the European Commission", the LSE said.
The sale would be conditional on the successful closing of the merger, both LSE and Euronext said.
The European Commission is concerned that the proposed merger would reduce competition in several financial market infrastructure areas.
By combining the exchanges of Germany, the UK and Italy, as well as several of the largest European clearing houses, it would create by far the largest European exchange operator, the Commission said in September.
Deutsche Börse is best known for operating the Frankfurt Stock Exchange but also runs other regulated exchanges, most notably the Eurex and EEX exchanges, trading various types of derivative products. Apart from trading its activities include the supply of post-trade infrastructure services such as clearing, settlement and custody services.
LSE operates the London Stock Exchange but also owns Borsa Italiana, the Italian stock exchange, and operates a number of other trading platforms for trading of stocks, other equity-like exchange traded products, bonds and derivatives. LSE is also active in the post-trading space, most notably in clearing through the London Clearing House and through Cassa di Compensazione e Garanzia, the Italian clearinghouse.
Shareholders in Deutsche Börse gave approval for the planned merger in July, after Deutsche Börse lowered the minimum acceptance threshold to make sure that the vote succeeded.
The public exchange offer made by the new holding company that is to be the parent of both LSE and Deutsche Börse had been subject to a minimum acceptance level of 75% of the shares in Deutsche Börse. This threshold was reduced to 60%.
The exchange operators agreed on the proposed £21 billion merger in February, and recommitted to the deal the day after the UK referendum on 23 June. Shareholders of the LSE then "overwhelmingly" voted to approve the merger on 5 July.