The additional early morning period would allow the exchange to target Asian markets and could require a physical expansion in the size of the trading ring, according to Reuters who cited three sources at ring-dealing firms.
However it is understood that discussions, which took place between a committee of ring-dealing representatives, are at an early stage and nothing has been decided. The LME declined to comment.
In June the market was bought by Hong Kong Exchanges and Clearing (HKEx), who agreed to pay $2.2bn (£1.4bn) for the 135-year-old institution.
The new owners are known to be keen to increase revenues but promised to maintain open-outcry trading until at least 2015 as part of their takeover offer.
Last week the exchange announced that September had been its busiest ever month.