The designs have been commissioned by the council to galvanise interest in a much-needed make-over for the West End tourist haven.
The council is desperate to turn the landmark into a family-friendly environment and exploit its potential entertainment uses.
Among the proposals currently on the drawing board are a new permanent stage and a larger entertainment area created by the removal of a statue at the centre of the square.
The local authority would also like to see new, modern street furniture and 'colour changing' lighting, to provide a constantly altering environment and bring activity to the area.
Councillor Simon Milton, leader of Westminster City Council, said: 'Home to British cinema and visited by up to 250,000 people a day, Leicester Square should be a stand-alone attraction in its own right for visitors to London.
'The plans we have will transform the square into a centre of entertainment in the West End, playing host to performances and exhibitions throughout the year. No longer just a walkthrough, the square will become an identified venue around the world for fun, family-friendly entertainment.
'For those who share our vision the opportunities are boundless,' Milton added.