Earlier this fall, the White House revoked CNN's Jim Acosta press credentials after a confrontation with an intern attempting to move the mic to another reporter.
"I am not aware that he is under consideration but, as I think all of us here would recognize, he would be great in any role that the president chooses to put him in", White House spokeswoman Sarah Sanders said of the news, which was also reported by CBS. "Mick M will do a GREAT job!"
One of the sources, speaking on condition of anonymity, said Kushner is now not inclined to pursue the position.
His successor Kelly, a former Marine general, was hailed for bringing military-style order and discipline to the president's office. "John will be staying until the end of the year".
Mulvaney, 51, rose to prominence as a founder of the powerful House Freedom Caucus conservative voting bloc. But his knowledge of Congress and how government works is likely to be an asset in the coming months.
Kelly was Trump's second chief of staff in just two years in a White House that has had extraordinarily high levels of turnover.
"Mick has done an outstanding job while in the Administration", Trump posted.
A former tea party congressman, Mulvaney was among a faction on the hard right that pushed GOP leaders into a 2013 government shutdown confrontation by insisting on lacing a must-pass spending bill with provisions created to cripple President Barack Obama's signature health care law.
Mulvaney said he was honored to have been selected. If they can not resolve an impasse with Congress, there will a partial government shutdown.
DC Mick Mulvaney Named Acting White House Chief Of Staff Former South Carolina congressman to take top post in Donald Trump’s administration
A senior administration official said there is "no time limit" for Mulvaney to remain in the top White House post.
Former Democratic President Bill Clinton elevated his OMB Director Leon Panetta to the job, as did former President Barack Obama with Jack Lew.
Key to his selection: Mulvaney and the president get along and the president likes him personally.
"The big question we all ask is, why is this temporary?" he told Reuters.
Nick Ayers, chief of staff to Vice President Mike Pence, was widely regarded as a leading candidate to succeed Kelly, but withdrew himself from the running.
As the choice still hangs in the air, U.S. media have revealed a number of possible nominees, among them Trump's son-in-law Jared Kushner, House Republican Mark Meadows, Treasury Secretary Steven Mnuchin and U.S. Trade Representative Robert Lighthizer. "I have so many people, I can not interview them all", he told Reuters in an interview on Tuesday.
Mulvaney also served as interim leader of the Consumer Financial Protection Bureau before the administration confirmed a permanent head for the agency.
President Trump has also appointed Elad Roisman as a commissioner for the US Securities and Exchange Commission (SEC).More news: Trump said to be considering son-in-law Kushner for chief of staff role