The denial comes after the Mail on Sunday reported that the former British prime minister met the president's son-in-law and key adviser, Jared Kushner, at the White House last week.
The paper claims the meetings were to discuss working for Mr Trump.
Mr Blair's office said the story was an "invention" and that he continues to work for peace "in a private capacity".
After he left Downing Street in 2007, Mr Blair took the role of Middle East envoy for the Quartet Group, made up of the European Union, US, Russia and United Nations.
His spokesman said: "Mr Blair has made no such 'pitch' to be the president's Middle East envoy.
"Neither has he had any discussions about taking such a role or any role working for the new president. He has been working on the peace process for 10 years.
"He continues to do so. He does so in a private capacity. He will continue to do it in that way. Period."
Mr Blair launched a campaign last month to try to persuade the British people to change their minds about leaving the European Union, following the Brexit referendum held last year.
Tony Blair has not pitched to become a Middle East envoy for US President Donald Trump, a spokesman has said.