The British Museum's former interim director said tourists should be charged £20 for entry.
Sir Mark Jones, 73, also called for the disputed Elgin Marbles to be shared with Greece.He said the charge might be needed to ensure the sustainability of the museum which is in need of an extensive £400m-£500m redevelopment.
The London attraction last year struck a controversial £50m deal with BP to fund renovation but Sir Mark - who took over last year - feels like more might be needed.
“The British Museum is also too small to do its job,” he told The Sunday Times.
“A master plan would include an increase in space and more space given over to facilities for visitors.”
In order to do this, he said: “The money has to come from somewhere, either a major part of the funding has to be found out of taxation, which is difficult as the public finances are very stressed, or we need to reasonably charge [tourists].”
At present, the museum is free for anyone looking to see the permanent collections but it does charge non members to see special exhibitions.
Sir Mark said a £20 charge would be “reasonable” considering The Louvre in Paris costing €22 per adult visitor while The Acropolis Museum in Athens is €15.
He added that entry for under 25s and British visitors should remain free. Under his plan, the admission fee could fund other projects and lower exhibition prices.
He also suggested that other major museums and galleries across the country, including the National Gallery, the Science Museum and the Natural History Museum, should also consider charging entrance fees to visitors from abroad."If we were ever to find a way to create a partnership with the Greeks over the Parthenon Marbles, we would need to find a way to fund it,” he added.
The marble statues came from friezes on the 2,500-year-old Parthenon temple and have been displayed at the museum for more than 200 years since they were removed by Lord Elgin when he was British ambassador to the Ottoman Empire in the early 19th century.
Some of the temple statues are on display in the Acropolis Museum in Athens and Greece has long called for the collections to be reunited.
Greece alleges the marbles were illegally acquired during a period of foreign occupation - which the UK Government and British Museum rejects
Sir Mark took over from Hartwig Fischer, who resigned as director in August after it was disclosed that 1,500 objects were missing or stolen from the museum's collection.
In March, Nicholas Cullinan, the director of the National Portrait Gallery since 2015, was announced as the permanent director of the museum.