According to a new biography, the titan of British art, who produced a collection of unforgettable and unsettling portraits, considered the proposal to be downmarket. Mr Freud has painted the likes of Kate Moss and the Queen.
It is believed the former Labour leader made an approach to the celebrated artist through a Cabinet ally.
In the new biography, The Lives of Lucian Freud by William Feaver, says: “When Labour came into power after the May 1997 election, the newly appointed Lord Chancellor, Derry Irvine, who saw himself as a connoisseur, made overtures regarding a portrait of Prime Minister Tony Blair.
“Lucian fended off that idea as being no better than the overtures concerning Princess Diana and those from Andrew Lloyd Webber and the newspaper tycoon Conrad Black proposing wife portraits.”
Despite facing the brush off by Mr Freud, the former Prime Minister was painted by artist Phil Hale in the final months of his premiership.
The image was unveiled in 2008.
A second image was painted by Alastair Adams in 2011, four years after Mr Blair left Downing Street, and hangs in London’s National Portrait Gallery.
Mr Freud died in 2011 at the age of 88 and was renowned for his nude portraits.
He famously painted a naked, pregnant Kate Moss back in 2002 and is believed to have tattooed the model’s two swallows on her lower back.
READ MORE: Lucian Freud painting hidden for DECADES could sell for £30,000
A 1995 nude of a civil servant called Benefits Supervisor Sleeping, was sold for a staggering £42million in 2015.
Born in 1922, Lucian Freud was one of the most significant painters of his generation and the grandson of the renowned psychoanalyst Sigmund Freud.
Just before WWII, he met sign painter Tom Wright while drinking in The Shoulder of Mutton in Hadleigh, Suffolk, where Wright was hanging a pub sign.
Freud befriended the local artisan and persuaded him to join the East Anglian School of Painting and Drawing, of which the artist was already a member.
Earlier this month, Mr Blair faced backlash after appearing on Sky News to outline his proposed coronavirus mass testing strategy.
Mr Blair insisted the expansion of testing capacities would ensure the UK is able to maintain the spread of the coronavirus under control without risking a new lockdown of the economy.
But his proposals were met with fury by members of the British public, who questioned why the former Prime Minister still receives air time.
Mr Blair insisted testing should be extended to all university students heading to school in the autumn to ensure there are no outbreaks in university towns.
He also insisted the Government has no more “excuses” about potential failures after months of the world grappling with the pandemic.