The temporary installation, titled "Blood Swept Lands and Seas of Red," has generated intense interest, with thousands lining up daily to look since it opened in August. Each of the 888,246 poppies represents a service member from Britain or its empire killed in the Great War.
Organizers estimate 4 million people will have visited the display by Tuesday, which is Armistice Day, the anniversary of the end of World War I on November 11, 1918.
But there have been calls from politicians and members of the public to keep the installation open longer.
Prime Minister David Cameron visited the site today, saying it had become a "much loved and respected monument."
Cameron said parts of the display, including a "wave" of poppies rising beside an entrance to the centuries-old Tower, would remain until the end of the month before going on a national tour.
They eventually will be preserved in the Imperial War Museum.