The Museum of London says it wants the Donald Trump baby balloon as an exhibit.
The blimp was flown over Parliament Square during the US President's working visit to the UK in July 2018.
Campaigners raised almost £18,000 to pay for the 6m-high (19.7ft) inflatable and London Mayor Sadiq Khan gave permission for it to fly.
The museum said the owners of the balloon were keen for it to go on display there.
Museum of London director Sharon Ament said it would also like to display a balloon depicting Mr Khan in a yellow bikini.
She said: "They're both really important and of their time."
Ms Ament said the blimps were "rich" objects, shedding light on "how people protest in London".
"It's extraordinary how some objects can capture the public imagination; certainly the balloon really did," she said.
The announcement comes as the Trump Baby blimp is expected to fly again during his state visit this week, which includes a private lunch with the Queen and a state banquet at Buckingham Palace.
Mr Trump will then meet Prime Minister Theresa May at St James's Palace on Tuesday morning for a business breakfast.
Protests at Mr Trump's visit, including "national demonstration" in Trafalgar Square, are planned for central London.
Both the Stop Trump Coalition and Stand Up to Trump protest groups said they would be present.
The Met Police said it had "a very experienced command team" leading the operation to deal with the visit.