's plan to could come at a hefty price. The former maximum security prison on an island in the Bay of San Francisco has been closed for more than 60 years which is today a major tourist hotspot, welcoming millions of visitors every year.
The ' Bureau of Prisons says Alcatraz was closed in 1963 as it was deemed "too expensive to continue operating". Its daily operating costs were high largely due to its remote location and at the time, an estimated $3-5 million was needed for the restoration and maintenance to keep it open - the equivalent of $52 million (£39 million) today. The President wants the prison "substantially enlarged and rebuilt".
An Alcatraz historian has warned the prison, which dates back to the mid-19th century, would require major work which would not come cheap.
John Martini told KRON 4: "It would be daunting, it would be astronomically expensive.
"You would have to add running water, sanitation, heating, electrical, it's all gone, there is some electricity but not enough to run the island.
"To take Alcatraz back and turn it into an operational penitentiary, using the building that is there now, would make as much sense as taking Fort Sumter, putting it back together and arming it with missile loading cannons."
Alcatraz was infamously difficult to escape from due to the strong ocean currents and cold Pacific waters surrounding it.
According to the FBI, in the 29 years Alcatraz was open, 36 men attempted 14 separate escapes - nearly all were caught or didn't survive the attempt.
It was known as "The Rock" and , including gangster Al Capone and George "Machine Gun" Kelly.
It has also been the subject of a number of movies.
wrote on his Truth Social platform that he wants a revamped Alcatraz to "house America's most ruthless and violent Offenders".
He said the prison 1.25 miles off 's coast has long been a "symbol of law and order".
Californian Democrat Nancy Pelosi, whose district includes the island, said 's plan is "not a serious one".
"It is now a very popular national park and major tourist attraction," she said on X.
Alcatraz Island is today operated by the National Park Service and is a designated National Historic Landmark.
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