The spokesperson told Sky News that Mr Blair had not met with the US President or discussed a role within his administration, but did not deny that he had met members of Mr Trump's team.
According to the Mail on Sunday, Mr Blair met the president's son-in-law and key adviser Jared Kushner at the White House last week to discuss working for Mr Trump.
The newspaper went on to claim Mr Blair has met Mr Kushner three times since September.
While in Downing Street, Mr Blair shared a close relationship with President George W Bush.
Despite winning three general elections, his role in leading Britain into the war in Iraq alongside Mr Bush badly damaged his legacy.
After leaving office in 2007, he took the role of Middle East envoy for the Quartet Group comprising the EU, US, Russia and UN until 2015.
Mr Blair has been making more interventions in UK politics since leaving his Middle East role.
Last month in a speech, he urged Remainers to "rise up" and persuade Brexit voters to change their mind about leaving the bloc.