The official says that Trump and Ayers could not agree on Ayers' length of service.
It is thought that Ayers, who has been seen as a potential candidate for office in Georgia, was reluctant to tie himself to Trump for what will be a hard final two years of his first term.
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Meanwhile, allies of Meadows, chairman of the conservative House Freedom Caucus, worked behind the scenes to make the case for the North Carolina congressman.
Trump is on pace to break that record, as he looks for his third chief of staff in less than 24 months.
"3 Chiefs of Staffs in less than 3 years of being President", Trump tweeted back in 2012. "You can not govern effectively without empowering a White House chief to execute your agenda and tell you hard truths".
The 36-year-old was seen as Mr Trump's main choice to replace Gen John Kelly, who will depart by the year's end.
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Mexico, in some form and there are many different forms, will reimburse us and they will reimburse us for the cost of the wall. She reportedly continued , "It goes to show you: You get into a tinkle contest with a skunk, you get tinkle all over you".
Ayers had told the president that he would do the job on an interim basis, through the spring.
With Ayers out of the running, Trump was considering four candidates for the post, including Office of Management and Budget director Mick Mulvaney, according to a person familiar with the president's thinking.
Trump has yet to announce who will replace Kelly.
Meadows' name has been mentioned on a number of lists speculating who will fill the post vacated by Kelly, the retired Marine general and Department of Homeland Security secretary.
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Luiz said he felt Chelsea had beaten "the best team in Europe at the moment". Two Premier League left-backs are being targeted by Marseille.
On Sunday, the United States president said that a decision would be made soon. But tension between the two men and between Kelly and other top officials had grown in recent months.
Pence said on Twitter that Ayers "has done an outstanding job as my Chief of Staff and I will always be grateful for his friendship, dedication to the @VP team and his efforts to advance the @POTUS agenda". He did have a military background wanting discipline, order, control, a style that does not match with President Trump's, who has run a private business the way he wanted to do it for many, many years.
Matthew Whitaker's current roles as acting attorney general will wrap up as soon as the Republican-controlled Senate approves General William Barr, President Trump's nominee for attorney general, leaving Whitaker available to take the job in the White House.
Kushner delivered some conciliatory remarks on Kelly during an appearance with Fox News host Sean Hannity on Monday night, saying Kelly "has served this country for over forty years".
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If there are multiple candidates, Conservative MPs hold a series of votes to choose two to go forward to a vote of party members. The pound fell briefly in response to news of the challenge to Mrs May, but later rallied.
Ayers had earned the backing of the president's influential daughter and son-in-law, White House advisers Ivanka Trump and Jared Kushner, but was viewed warily by other aides.