According to The Mail on Sunday newspaper, Blair met with Trump's son-in-law and key advisor Jared Kushner last week to discuss working for the Republican president.
The weekly tabloid said Blair had met Kushner three times since September.
A spokesman for Blair said: "I'm not going to comment on private conversations."
Blair, who led the centre-left Labour Party, was Britain's prime minister from 1997 to 2007.
Despite being from the opposite side of politics, he enjoyed close relations with Republican US president George W. Bush.
Blair won three general elections but his role in leading Britain into the war in Iraq alongside Bush has badly damaged his legacy at home.
After leaving office, Blair was the envoy of the Middle East Quartet until 2015.
The group comprises the European Union, Russia, the United Nations and the United States.
Blair has been making more interventions in British politics since leaving his Middle East role.
Last month he urged Britons who support the European Union to "rise up" and persuade Brexit voters to change their mind about leaving the bloc, in a high-profile speech.
He also slapped down the "utter hypocrisy" of a report last month in The Mail on Sunday's sister title, the Daily Mail, about the release of a Guantanamo detainee.
Blair wrote an article in The New York Times newspaper on Friday where he called for a centrist new coalition that is "popular, not populist", in order for liberal democracy to survive and thrive in the face of rightist populism.
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