Ayers, 36, is the father of three young children and had reportedly planned to leave the administration at the end of this year and return to his home in Georgia.
Ayers thanked Trump and announced he was leaving the White House at the end of the year on Sunday.
Trump announced Saturday that Kelly would be departing the White House around the end of the year.
Sources told Reuters Mr Ayers would join a political action committee, assisting the President from outside the administration.
Ayers revealed the news in a tweet.
The Wall Street Journal first reported Ayers was out of the running.
On Sunday afternoon Nick Ayers, now chief of staff to Mike Pence, tweeted his thanks to Trump, the vice-president "and my great colleagues for the honor to serve our Nation at The White House".
Also emerging as a candidate is Rep. Mark Meadows, a North Carolina Republican and the chairman of the House Freedom Caucus.
"I think Donald Trump desperately needs in that job someone who can walk into the Oval Office, close the door, and tell him what he does not want to hear", Whipple said. Ayers was said to be out after only being willing to commit to staying until next spring while the president found a more permanent replacement.
Mr. Trump brought Mr. Kelly in past year to restore order to the White House, but has clashed repeatedly with the retired Marine Corps general in recent months.