El-Erian, the chief economic advisor at Allianz, would bring a wealth of experience to the position, including his time at bond giant Pimco.
El-Erian would take the seat vacated in October by Stanley Fischer and presumably would be second in command to Jerome Powell. President Donald Trump recently nominated Powell to take the chairman's position at the central bank when Janet Yellen's term expires in February. The nomination awaits Senate confirmation.
The search process has just begun and the vice chair announcement is not likely this year, said CNBC's source, who is familiar with the discussions.
This is not the first time El-Erian's name has come up for a prominent position outside of the private investing community. In 2012, he was mentioned as a possible prime minister for his native Egypt. Dow Jones first reported El-Erian was in the Fed running Tuesday.
"El-Erian would bring to the Fed Board deep understanding of financial markets and the interaction of policy with markets, as well as a global perspective often missing from Fed policy debates," Krisha Guha, head of global policy and central bank strategy at Evercore ISI, said in a note.
Guha described El-Erian as likely to be "slightly hawkish" on monetary policy, meaning he may favor higher rates and a faster runoff of the Fed's balance sheet. Guha said other candidates for the vice chair job that "might plausibly be considered" include Glenn Hubbard, the Columbia Business School dean, and current San Francisco Fed President John Williams.
In addition to the El-Erian appointment, the White House is considering the nomination of Michelle Bowman, a Kansas banking regulator, for another Fed governor appointment, according to Dow Jones. The report said the administration is looking for someone with monetary policy experience to guide the central bank.
Trump has three openings on the seven-member Fed board of governors — four if Yellen decides not to stay on after her term at the helm expires. On top of those vacancies, the critical New York Fed president's position also is open. However, that seat is filled internally.
Neither El-Erian nor the White House responded to requests for comment.
El-Erian would bring some name recognition to the otherwise low-key and taciturn central bank.
His market pronouncements are closely watched, and he's remembered as coining the term "new normal" when he was the CEO at Pimco. The Newport Beach, California-based firm once ran the largest bond fund in the world but has seen its assets decline since the high-profile departures of El-Erian and the firm's founder, Bill Gross.
El-Erian also served as deputy director at the International Monetary Fund.