Icahn added in a statement that he was surprised Trump was running for president and "even more surprised that he stated he would make me Secretary of Treasury."
Read MoreDonald Trump announces candidacy for president
Trump announced his preference for Ichan on Thursday on MSNBC, two days after he launched his campaign for the country's top office.
Ichan also said he applauded Trump for raising the issue of low interest rates. "Never in the history of the Federal Reserve have interest rates been artificially held down for so long at the extremely low rates existing today," he said.
Read MoreTrump turns GOP race into reality-TV circus
Nevertheless, the former Republican National Committee Chief, Michael Steele, told CNBC's "Squawk Box" that Trump's candidacy was a point of concern for the GOP establishment.
"I don't think he ultimately wins, but he does change the nature of the conversation. And one of the challenges the GOP field will have will be allowing Donald Trump to dominate what the topics of discussion are," Steele said. "Candidates don't want cameras put in their face asking them do you agree with Donald Trump that Mexicans are rapists."
Read More Mexico to Trump: You are one 'ignorant,' 'prejudiced'
Steele was referring to a comment Trump made during his campaign launching speech in which he said "When Mexico sends its people, it is not sending its best ... They're sending people that have lots of problems, and they're bringing those problems with us. They're bringing drugs. They're bringing crime. They're rapists."
—CNBC's Matthew J. Belvedere contributed to this report.