A Banksy mural showing a star being chiselled from the EU flag could be removed and sold, the owners have said.
The artwork appeared near Dover's ferry terminal on Sunday on a building that is due to be demolished.
The Godden family, which owns the property, said they were looking at options with the Bankrobber Gallery in London for the latest Banksy creation.
The family previously lost a High Court battle after trying to sell another mural by the artist that they owned.
The Goddens said: "We are exploring options for the retention, removal or sale of the [Dover} piece.
"We will look to benefit local charities with proceeds from any sale of the piece," added the family, which has a large property portfolio.
Dover District Council has said it will be using CCTV to monitor the artwork, on York Street, after it was defaced.
In 2014, a Banksy mural of a woman staring at an empty plinth was painted on a wall of an amusement arcade, also owned by the Godden family.
The work entitled Art Buff was shipped to the USA to be sold, but was returned to Folkestone in 2015 after a lengthy High Court battle.