President-elect Donald Trump is set to meet Monday with former Texas Gov. Rick Perry and Oklahoma Gov. Mary Fallin, both of whom could be under consideration for top-level positions in the new administration.

Mr. Perry, a former 2016 GOP rival of Mr. Trump’s, is a possible choice for secretary of Energy or secretary of Defense and Ms. Fallin could be considered to lead the Interior Department, former Trump campaign manager Kellyanne Conway said on “Fox & Friends.”

Ms. Conway said there will “possibly” be more announcements Monday.

“But the fact is we’re way ahead of schedule,” she said.

Mr. Trump is also meeting Monday with Rep. Tulsi Gabbard, Hawaii Democrat, former Sen. Scott Brown of Massachusetts, former House Speaker Newt Gingrich and former Secretary of Labor Elaine Chao.

Also on the Monday schedule are National Border Patrol Council President Brandon Judd, National Immigration and Customs Enforcement (ICE) Council President Chris Crane and Indiana State Health Commissioner Jerome Adams.

Over the weekend at his golf club in Bedminster, New Jersey, Mr. Trump met with former Massachusetts Gov. Mitt Romney, retired Gen. James Mattis, New Jersey Gov. Chris Christie, former New York City Mayor Rudolph Giuliani and Kansas Secretary of State Kris Kobach, among others.

Mr. Trump is back in Trump Tower in Manhattan on Monday as he works to fill out the rest of his administration. He has already named retired Lt. Gen. Michael Flynn as national security adviser and has selected Sen. Jeff Sessions to be attorney general and Rep. Mike Pompeo to be CIA director.

The U.S. Senate has to confirm Mr. Sessions and Mr. Pompeo for their respective positions.

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