This comes as Prince Andrew today released a statement after new footage emerged showing him inside the convicted paedophile's Manhattan mansion on December 6, 2010.
Even before Epstein's conviction in 2008, staff at Buckingham Palace had long discussed his friendship with Andrew and why they believed he was someone to be kept away from the Duke.
'His Royal Highness deplores the exploitation of any human being and the suggestion he would condone, participate in or encourage any such behaviour is abhorrent'.
Epstein committed suicide in a Manhattan jail cell earlier this month while being held on sex-trafficking charges.
Kirsty Wark speaks to former BBC Royal Correspondent, Michael Cole.
The source said they 'phoned Andrew and told him, "You can not have a relationship with Jeffrey"' after Epstein was convicted. Police arrested him in July after he landed in New Jersey on his private jet.
A picture of Andrew and Epstein strolling in Central Park from around the same time surfaced in 2011, prompting questions over Andrew's judgment.
At the time, the duke was the U.K.'s special representative for trade, a role he quit the following year.
Meanwhile, the duke could face further pressure with the release of more court documents relating to British socialite Ghislaine Maxwell, who is alleged to have "acted as a madam" for her lover Epstein, The Telegraph reported.
Buckingham Palace has issued strong denials over claims from a woman who said she was forced to have under-age sex with the duke.
The duke was photographed with Epstein in New York's Central Park in 2010 after the tycoon had served his 18-month prison sentence for soliciting a minor for prostitution.
But the allegations were struck from the record by a United States judge in 2015, who said the "lurid details" were not needed to decide a civil case concerning Epstein.
Buckingham Palace has said Giuffre's allegations are "false and without any foundation" and that any suggestion Andrew ever engaged in sex with minors is "categorically untrue".
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