President-elect Donald Trump will be back in the saddle Monday in New York as he looks to decide who will fill the integral appointments in his Cabinet as concerns about a possible secretary of state choice rise and the distraction of a recount vote in Wisconsin, and possibly other key battleground states, set to press on.

Trump has a series of meetings scheduled to try and narrow down the foundation of his Cabinet after spending Thanksgiving weekend at his Palm Beach, Fla., estate. As the talks are reportedly expected to intensify over the course of the week, concerns about the possible appointment of Mitt Romney as secretary of state were made known on Sunday.

Top adviser Kellyanne Conway said Sunday that she will support Trump's pick, but continues to argue that the grass-roots supporters who backed his improbable victory feel let down about Romney, considering he called Trump a “con man” and a “phony.”

"People feel betrayed to think that … Romney, who went out of his way to question the character and the intellect and the integrity of Donald Trump … would be given the most significant Cabinet post of all,” Conway said on NBC's "Meet the Press.”

Trump and his team of advisers appear to be split on whether Trump should pick Romney, a former GOP presidential nominee, or former New York Mayor Rudy Giuliani, an early Trump loyalist.

Incoming White House Chief of Staff Reince Priebus on “Fox News Sunday” downplayed rumors over vicious infighting over who will lead the State Department, saying that Trump's "going to make the best decision for the American people.”

Former House Speaker Newt Gingrich told “Fox & Friends Sunday” that a Romney choice would be disappointing, adding, "I think there's nothing Mitt Romney can say that doesn't sound phony and frankly pathetic.”

Romney was one of the most notable Republicans to speak out against Trump during his campaign.

People involved in the transition process told the Associated Press Trump's decision on his secretary of state did not appear to be imminent. Former New York City Mayor Rudy Giuliani, Tennessee Sen. Bob Corker and John Bolton, a former ambassador to the U.N., have also been under consideration.

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Meanwhile, looming in the background of Trump’s Cabinet picks is the recount that is slated to take place in Wisconsin. State election officials are expected to meet Monday to discuss a possible timeline for a recount of the state’s presidential election.

The recount comes at the request of Green Party candidate Jill Stein, who says it’s important to determine whether hacking may have affected the results. Stein also plans to request recounts in Pennsylvania and Michigan.

Trump went on a Twitter offensive Sunday in an attempt to assail that the recount front. He claimed widespread voter fraud in his storm of tweets.

"I won the popular vote if you deduct the millions of people who voted illegally," Trump tweeted in the afternoon before alleging in an evening tweet "serious voter fraud in Virginia, New Hampshire and California."

Trump narrowly won Wisconsin and Pennsylvania and, as of Wednesday, held a lead of almost 11,000 votes in Michigan, with the results awaiting state certification Monday. All three would need to flip to Hillary Clinton to upend the Republican's victory, and Clinton's team says Trump has a larger edge in all three states than has ever been overcome in a presidential recount.

There's been no evidence of widespread tampering or hacking that would change the results; indeed, Clinton's team said it had been looking for abnormalities and found nothing that would alter the results.

Clinton's lawyer Marc Elias said her team has been combing through the results since the election in search of anomalies that would suggest hacking by Russians or others and found "no actionable evidence." But "we feel it is important, on principle, to ensure our campaign is legally represented in any court proceedings and represented on the ground in order to monitor the recount process itself," he said.

The Associated Press contributed to this report.