President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE on Tuesday said he would announce his next White House chief of staff in a "week or two," adding he is in "no rush" to choose a successor to John Kelly John Francis KellyMORE.

Speaking to reporters in the Oval Office, Trump pushed back on the notion he is struggling to find a new top aide after his first choice, Nick Ayers, turned down the position.

"We have a lot of people who want the position," Trump said.

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His comments came after a heated conversation with House Minority Leader Nancy Pelosi Nancy PelosiHoyer: House should vote on COVID-19 aid — with or without a bipartisan deal Ruth Bader Ginsburg lies in repose at Supreme Court McCarthy threatens motion to oust Pelosi if she moves forward with impeachment MORE (D-Calif.) and Senate Minority Leader Charles Schumer Chuck SchumerCruz blocks amended resolution honoring Ginsburg over language about her dying wish Senate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' MORE (D-N.Y.) over funding for a border wall. They mark the first time Trump has addressed the chief of staff vacancy in person since Ayers's surprise decision over the weekend to not take the job.

The president did not specify who he was considering for the role, other than to say a lot of friends of his want the job, as do "people that Chuck and Nancy know."

Several news reports over the last 24 hours have characterized Trump as scrambling to find an alternative pick. Sources told The Hill that there was no clear plan B after Ayers, who is currently Vice President Pence's chief of staff, said he will leave the administration soon to work for a pro-Trump super PAC.

Potential candidates for the job that have been reported in recent days include Rep. Mark Meadows Mark Randall MeadowsThe Hill's Morning Report - Sponsored by Facebook - GOP closes ranks to fill SCOTUS vacancy by November House moves toward spending vote after bipartisan talks House Democrats mull delay on spending bill vote MORE (R-N.C.), Treasury Secretary Steven Mnuchin Steven Terner MnuchinHillicon Valley: DOJ proposes tech liability shield reform to Congress | Treasury sanctions individuals, groups tied to Russian malign influence activities | House Republican introduces bill to set standards for self-driving cars Treasury: Trump's payroll tax deferral won't hurt Social Security Treasury sanctions individuals, groups tied to Russian malign influence activities MORE, U.S. Trade Representative Robert Lighthizer Robert (Bob) Emmet LighthizerWhiskey, workers and friends caught in the trade dispute crossfire GOP senator warns quick vote on new NAFTA would be 'huge mistake' Pelosi casts doubt on USMCA deal in 2019 MORE and Office of Management and Budget Director Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE.

Meadows said on Monday that it would be an "incredible honor" to be chosen as chief of staff, and Bossie appeared on Fox News Tuesday morning and appeared to lay out his credentials for the job.

The other candidates have reportedly indicated they'd prefer to stay in their current roles.

Trump announced on Saturday that Kelly would leave his role as chief of staff at the end of the year, marking the end of a 17-month tenure that was marked by frequent reports of tensions with the president.

Kelly's replacement will become Trump's third chief of staff during his less than two years in the White House. Kelly replaced the president's first top aide, Reince Priebus Reinhold (Reince) Richard PriebusLeaked audio shows Trump touted low Black voter turnout in 2016: report Meadows joins White House facing reelection challenges Trump names Mark Meadows as new chief of staff MORE, in July 2017.

Updated at 12:46 p.m.