"Mr Blair has made no such 'pitch' to be the president's Middle East envoy," a 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."

Andrew Bridgen, a Conservative MP, told The Telegraph: "It's often said that a wise man should try to learn from the mistakes of history so as not to repeat them."

After leaving Downing Street, Mr Blair took the role of Middle East envoy for the Quartet, an organisation comprising the EU, US, Russia and the UN, that aims to help negotiations in the Middle East.