The Metropolitan Police said on Sunday it was "actively looking into" media reports that Andrew sought information in 2011 to smear Giuffre by asking an officer on the force to find out if she had a criminal record.
The report by the Mail on Sunday followed Buckingham Palace's announcement on Friday that Andrew agreed to relinquish use of the Duke of York and other remaining royal titles after emails emerged showing he had remained in contact with convicted sex offender Jeffrey Epstein longer than he previously admitted.
Giuffre's family welcomed news of the duke's demise but said King Charles III should go further and strip Andrew's title as prince.
Giuffre died by suicide in April at the age of 41.
The emails were the last straw for the House of Windsor after years of tawdry headlines about Andrew's dodgy friends and suspicious business deals.
The move to insulate the monarchy from Andrew's scandals has been ongoing since November 2019 when he gave up all of his public duties and charity roles after a disastrous interview when he sought to counter media reports about his friendship with Epstein and deny allegations that he had sex with a 17-year-old Giuffre, who was trafficked by Epstein in 2001.
Andrew was widely criticised for failing to show empathy for Epstein's victims and for offering unbelievable explanations for his friendship with the disgraced financier.
The BBC interview, in which he said he cut off contact with Epstein in 2010, came back to haunt him and sowed the seeds for his dukedom demotion when emails emerged last week showing he emailed Epstein on February 28, 2011.
Andrew told Epstein in the note that they were "in this together" and would "have to rise above it".
The Mail reported that in 2011, as the newspaper was about to publish a now-infamous photo of the prince with his arm around the partly bare midriff of Giuffre, Andrew provided his bodyguard with Giuffre's date of birth and confidential social security number to find out if she had a checkered past.
It's not clear if the officer complied with the request. Giuffre's family said she didn't have a criminal record.
With that report and Giuffre's posthumous memoir being published on Tuesday, the scandal will not soon evaporate.
British Energy Secretary Ed Miliband, who was serving as the government's representative on the Sunday morning news programs, said a police officer should not be enlisted in a smear campaign.
"These are deeply concerning allegations," Miliband told the BBC.
"I think people want to look at those allegations and what the substance is behind them. But if that is correct, that is absolutely not the way that close protection officers should be used."
Andrew in 2022 reached an out-of-court settlement with Giuffre after she filed a civil suit against him in New York.
While he didn't admit wrongdoing, Andrew did acknowledge Giuffre's suffering as a victim of sex trafficking.
In his statement on Friday, Andrew said he continues to "vigorously deny" the accusations.
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