A photograph printed by the Daily Telegraph appears to show the British socialite reclining in the ceremonial chair next to actor Keven Spacey in 2002.
They were on a private tour of the palace organised by the Duke of York for former US president Bill Clinton, according to the newspaper.
It comes after Maxwell was arrested in New Hampshire on Thursday over allegations she helped disgraced financier Jeffrey Epstein, her former boyfriend, "identify, befriend and groom" girls, including one as young as 14.
Epstein was not on the palace tour when the picture was taken, the Telegraph said. Buckingham Palace declined to comment.
The thrones in the photograph match those in the Throne Room at Buckingham Palace, as pictured on the Royal Family website.
Ms Maxwell was a close friend of Prince Andrew, having known him since university, and is said to have introduced him to Epstein.
She also features in the background of a photograph which apparently shows the duke with his arm around Virginia Giuffre, who has claimed the prince had sex with her in London in 2001, when she was 17.
Prince Andrew is now being urged to provide information to the FBI in relation to the investigation into Ms Maxwell, after she appeared in court accused of facilitating Epstein's sexual exploitation of underage girls between 1994 and 1997.
However, a lawyer for dozens of Epstein's alleged victims has accused him of “deliberately evading authorities” and a US prosecutor described him as “falsely portraying himself as willing and eager to cooperate”.
The Duke categorically denies he had any form of sexual contact or relationship with Ms Giuffre, while his lawyers have insisted the duke has repeatedly offered to provide a witness statement to the investigation.
On Thursday, Maxwell was ordered to remain in custody by a magistrate while she is transferred to New York for a detention hearing.
Four of the six charges cover Maxwell's dealings with Epstein from 1994 to 1997, when she was in an "intimate relationship" with him, according to the indictment.
These include conspiracy to entice minors to travel to engage in illegal sex acts and enticement of a minor to travel to engage in illegal sex acts.
She is further charged with conspiracy to transport minors with intent to engage in criminal sexual activity and transportation of a minor with intent to engage in criminal sexual activity.
Authorities also claim that Maxwell, who is also charged with two counts of perjury, lied when being questioned under oath in 2016.
She has previously denied any wrongdoing or knowledge of sexual misconduct by Epstein.
Additional reporting by Press Association