"I am flattered but do not get up early enough in the morning to accept this opportunity," Icahn, 79, said in a public statement after Trump, 69, told cable station MSNBC that Icahn could be a dream Treasury pick if he wins the White House in the 2016 presidential election.

Trump joined a large Republican field by announcing his candidacy earlier this week with a promise to make the United States great again and warning of an impending economic and financial bubble.

This may be music to Icahn's ears after the man who commands the attention of financial markets and has long tangled with corporate chief executives himself predicted an eventual stock market sell off after years of gains fueled by low interest rates.

"I personally believe we are sailing in dangerous unchartered waters," Icahn said on Friday. He praised Trump for warning new audiences about a "big fat bubble coming up" and said more people should be discussing this matter.

Also this week Former Florida Gov. Jeb Bush announced his plans to seek the Republican nomination joining U.S. senator from Kentucky Rand Paul and U.S. senator from Florida Marco Rubio and others battling for the nomination.

Trump complained on MSNBC that America does not have the "best or brightest" negotiators working on trade deals and said he would turn to Wall Street for extra help. Trump also named former General Electric CEO Jack Welch and investor Henry Kravis as other advisors if he were to win an election.

Icahn who has been able to vote for president since the Dwight D. Eisenhower era, said he was "extremely surprised to learn that Donald" is running for president and even more surprised "that he stated he would make me Secretary of Treasury." Most analysts have said that Trump, who has never held elective office, is unlikely to win the Republican nomination.

Also this week Former Florida Gov. Jeb Bush announced his plans to seek the Republican nomination joining Rand Paul, U.S. senator from Kentucky, and Marco Rubio, U.S. senator from Florida and others battling for the nomination.