The White House is expected to announce the decision later on Wednesday or on Thursday, media reports said.
Middle East priority
Aaron David Miller, a former US Middle East negotiator and analyst, told the Associated Press that Mitchell's appointment reflected "serious commitment by the new administration to addressing the Arab-Israeli crisis".
"He has real negotiating experience in Northern Ireland and the Middle East and he understands the requirements of both sides," he added.
Obama, who was inaugurated as US president on Tuesday, made phone calls to several key leaders in the Middle East on Wedneday as the region continued to deal with the aftershocks of Israel's offensive in Gaza.
These included Hosni Mubarak, Egyptian president, Ehud Olmert, the Israeli prime minister, Jordan's King Abdullah and Mahmoud Abbas, the Palestinian president, Robert Gibbs, the White House press secretary, said.