Lee Kuan Yew International Airport? A banknote with the founding Singaporean leader's face on it? A new public holiday?

The death of the widely revered leader known as "LKY" last month has sparked a vigorous debate in Singapore over how to honour its first prime minister, who famously disdained personal monuments.

His son, Prime Minister Lee Hsien Loong, has called for further reflection on how best to remember the late leader, whose death sparked an unprecedented outpouring of grief in the city-state, saying any decision must "stand the test of time".

Lee, who died on March 23 aged 91, refused to allow statues of himself and rarely lent his name to institutions, despite dominating politics for half a century - setting him apart from other post-colonial Asian leaders.

In his will, the widower instructed his children to destroy their old bungalow after he died, fearing it would be turned into a relic with people tramping in and out of their former private quarters.

But fresh calls to preserve it as a museum surfaced after the death of Lee, who was given a hero's funeral for transforming Singapore into one of the world's richest and most stable societies with his iron-fisted rule from 1959 to 1990.

The government will make a final decision on the house's fate only after Lee's only daughter, neurologist Lee Wei Ling, stops living there - and there are no immediate plans for her to leave.

Some Singaporeans want coins, or banknotes - which currently depict the country's first president, Yusof bin Ishak - to bear Lee's image.

Politicians and members of the public have called for leading hub Changi Airport, named after the eastern suburb where it is built, to be renamed after Lee.

An online petition to erect a statue of Lee has gained little traction, however, with many Singaporeans wary of going against their late leader's wishes.

Writing in the Straits Times a few weeks after her father's death, Lee Wei Ling said she was "baffled" by reports that MPs were suggesting naming structures and institutions after her father.

The senior Lee "had worked hard to prevent any personality cult from growing around him", she wrote.