The former Prime Minister was said to have met Mr Trump’s son-in-law, Jared Kushner, three times in recent months, including a three-hour encounter in the West Wing of the White House.
The Mail on Sunday reported Mr Blair wanted to become a Middle East peace envoy for the President. It is a role he held for eight years representing the Quartet of powers (the UN, the US, the EU and Russia) seeking to mediate the Israeli-Palestinian peace process, before he stepped down in 2015.
The ex-Labour leader's office said it did not comment on private meetings.
A statement read: “The story in the Mail on Sunday is an invention. 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.”
The Mail on Sunday reported that Mr Blair met Mr Kushner, who is now an adviser to the President, for the first time in September last year. They reportedly met a second time in November after Mr Trump’s election win, ahead of the latest apparent encounter in Washington.
The President has put Mr Kushner in charge of brokering a peace deal between the Israelis and Palestinians.
During Israeli Prime Minister Benjamin Netanyahu’s visit to Washington, Mr Trump suggested his administration would no longer insist on the creation of an independent Palestinian state as part of any peace accord.
While he later expressed his preference for the option, he repeated that he would be “satisfied with whatever makes both parties happy”.
Former Secretary of State John Kerry had the Obama administration’s last word on the conflict, when he said he feared the two-state solution was “in peril”.