The consultation paper sought feedback on five options: four covering shorter hours, and a fifth on making no changes to the trading day that currently starts at 0800 local time (0700 GMT in summer) and ends at 1630.
Options include opening 30 minutes to an hour later, and closing up to an hour earlier. It also proposes cutting the number of "auctions" during the trading day from five to three.
"There is a general sentiment that a coordinated approach by European exchanges would be required in order for a change to be effective," the LSE said.
Regulatory approval would be needed for any change to go ahead, it added.
The Investment Association, which represents asset managers, said it was very pleased that the LSE had listened to traders' calls.
"We need to call time on the long hours culture, which is detrimental to diversity and mental health, and inefficient for the markets," said Galina Dimitrova, the IA's director for investment and capital markets.
The public consultation ends on Jan. 31.
Europe has the longest stock trading hours in the world, between eight and 10 hours, compared to 6-8 hours on Wall Street and Singapore.
The potential benefits of shorter hours include concentrating liquidity, helping to encourage diversity of staff, and a positive impact on mental wellbeing of staff, the consultation paper said.
Traders say shorter hours would cut the overlap in trading hours with the United States and have far reaching benefits for traders, but could drive some business to exchanges outside Europe.
It is unclear if all main exchanges in Europe would back shorter hours.
(Reporting by Huw Jones, Editing by Lawrence White and Emelia Sithole-Matarise)
By Huw Jones