Senior figures including Boris Johnson and Defence Secretary Philip Hammond have indicated support for a new monument to the former prime minister in the heart of the capital.
A spokesman for the London mayor said it would be a "fitting honour for the greatest peacetime prime minister of the 20th century".
David Cameron has welcomed the suggestions, but insisted now is not the time to make a decision.
Sources have played down the prospect of the statue going on the vacant plinth in Trafalgar Square, pointing out it is already successfully hosting artworks.
Len Duvall, leader of the Labour group on the London Assembly, has warned that that location would be "inappropriate" and "crass triumphalism".
Instead, the mayor's office, Westminster Council and Government are looking at a variety of central London sites, including Parliament Square.
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