Back in March, the artist created a mural on the wall of the prison displaying a man dressed in prisoners' clothing scaling down the wall with a rope made from the scroll of a typewriter.
Many believe that this portrait is of famous poet and playwright, Oscar Wilde who served time at the prison between 1895-1897.
Campaigners hope that this sale will prevent the Grade-II listed building from being sold to housing developers.
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Banksy said: "I had very little interest in Reading until I was on a rail replacement bus service that went past the jail.
"It's rare to find an uninterrupted 500m-long paintable surface slap bang in the middle of a town; I literally clambered over the passenger next to me to get a closer look.
"I promised myself I'd paint the wall even before I knew what it was - I'm passionate about it now, though.
"Oscar Wilde is the patron saint of smashing two contrasting ideas together to create magic. Converting the place that destroyed him into a refugee for art feels so perfect we have to do it."
Wilde spent time in the prison formally known as Reading Gaol from 1895 to 1897 after being convicted with gross indecency when his affair with Lord Alfred “Bosie” Douglas was exposed.
The stencil soon up for sale was last displayed earlier this month at Bristol Museum and Art Gallery as part of an exhibition by the artist Grayson Perry for his Channel 4 series Grayson’s Art Club.
Matt Rodda, Labour MP for Reading East, has said that the concept of using the prison to house arts has been proved by past exhibitions which he planned to raise an urgent question in Parliament this week to put ministers “on the spot” with the offer.
He also said: “There are these amazing layers of history – there’s the literary history and the LGBT community history, and the link to Oscar Wilde. But there’s also some local and national Victorian social history and there’s the link to the Royal Family all in one building and it’s so well connected to the rest of the country.
“For so many reasons it’s absolutely right this building is preserved and used in a constructive way rather than just being gutted and turned into flats or some other thing.”
Jason Brock, Reading Borough Council leader, said: “We very much welcome the attention that Banksy’s interest in Reading Gaol has placed on both the Ministry of Justice’s sale of the vacant prison and on the council’s ambition to transform it into a hub of arts, heritage and culture of local and national significance.
“The council has had only informal approaches from representatives of Banksy to date, but no detailed discussions.
“Our bid remains firmly on the table and has widespread support – both from within the community here in Reading and from the wider arts, heritage and cultural community – all of whom recognise the prison’s huge historical and cultural value.”
The Ministry of Justice said: “The deadline for bids has passed and we are currently considering the ones we received.”
Becky Buckle is Mixmag's Digital Intern, follow her on Twitter