The former Prime Minister met the US president’s son-in-law and key adviser Jared Kushner at the White House last week, according to the Mail on Sunday.
It was claimed by the newspaper that Mr Blair was seeking to become the president’s Middle East peace envoy and had met Mr Kushner three times since September.
But a spokesman for Mr Blair said the story was an "invention" and that he had made no such "pitch" to the White House.
"Mr Blair has made no such 'pitch' to be the president's Middle East envoy," the spokesman said.
"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’s spokesman had earlier refused to be drawn on the claims, saying: “I’m not going to comment on private conversations."
After leaving Downing Street, the former Labour leader took the role of Middle East envoy for the EU, US, Russia and the UN.
He stepped down from the position in 2015 after almost eight years in the role.
Following Mr Trump's victory in the election, Mr Blair admitted that the result was an "earthquake" but that his success was a "reality" that politicians in the West had to come to terms with.
After Prime Minister Theresa May invited the new president to make a controversial state visit to the UK, he said he did not criticise her for "reaching out" and that it was important that the two leaders built a strong relationship.