New York: Donald Trump stepped up his contentious search for a secretary of state on Tuesday before he ditches cabinet interviews later this week to lead a victory tour kicking off in the swing state of Ohio.

The billionaire's nominee for the job will be America's public face to the rest of the world, the person who will succeed John Kerry, head up a department of 70,000 staff and lead the largest diplomatic operation in the world.

The prospective candidates touted most frequently have been erstwhile Trump critic and former Massachusetts governor Mitt Romney, celebrated general yet scandal-clad former CIA director David Petraeus, Senate Foreign Relations Committee chairman Bob Corker and outspoken former New York mayor Rudy Giuliani.

Aides say Trump is ahead of schedule in unveiling cabinet picks, mostly recently fierce Obamacare critic Congressman and former surgeon Tom Price as health secretary and Elaine Chao as transportation secretary -- both nominated Tuesday.

But all eyes are on a trio of key posts that remain to be decided: the secretaries of defense, state and treasury -- for which US media reported that Trump's was expected to name former Goldman Sachs investment banker Steven Mnuchin as early as Wednesday.

The Wall Street Journal also reported, citing a transition official, that Wilbur Ross, a billionaire investor known for taking over ailing industrial firms and selling them for a big profit, would be named as commerce secretary.

For the top diplomat brief, Trump held talks Tuesday with Senator Corker, considered a safe pick without the baggage of Petraeus and unfettered by Romney's history of disloyalty to the billionaire.

Corker, 64, said after the meeting that he thought Trump had narrowed the choice "to a very small group of people" and it was important that the president-elect selects somebody on the same wave length.

"This is a decision that he needs to make," the Tennessee senator told reporters. "He needs to choose someone that he's very comfortable with and he knows that there's going to be no daylight between him and them."

He said that Trump did not discuss a timeline for announcing his pick. "I think he'll make the decision when he's comfortable," said Corker.

- Petraeus 'premature' -

Romney, 69, a favorite among establishment Republicans, is expected to dine with Trump on Tuesday for a second face-to-face meeting in 10 days.

But some among Trump's inner circle are horrified at the prospect of rewarding with such a plum job an outspoken critic who castigated the real estate tycoon during the campaign as a "fraud" and a "conman."

His distrust of Russia -- at odds with a president-elect who has spoken admiringly of Vladimir Putin -- would also reassure establishment Americans.

Best known as the Republican nominee who lost the 2012 election to Barack Obama, Romney managed the 2002 Winter Olympics in Salt Lake City and was a successful businessman before going into politics.

Petraeus, who met the president-elect at Trump Tower in New York on Monday, has by far the most foreign policy experience of the lot.

"Very impressed!" tweeted Trump just minutes after the meeting. The 64-year-old scholar-warrior commanded troops in Iraq and Afghanistan, was credited with masterminding the Iraq surge and became head of the CIA in 2011.

But his glittering public career came crashing to a halt in 2012 when he resigned from the CIA after showing classified material to his mistress and biographer Paula Broadwell. 

Trump spokesman Jason Miller told Fox News Radio that it "might be a little bit premature" to assume Petraeus is being considered.

- Victory tour -

His appointment would arouse accusations of hypocrisy after Trump savaged Hillary Clinton for mishandling classified emails, but experts do not believe the scandal is insurmountable given the respect he commands on Capitol Hill.

Republican Senator Lindsey Graham told reporters on Tuesday that he was "a big fan" of Petraeus. Republican Senator John McCain, another Trump critic, said he would "love" to see him return to public service.

Giuliani, who campaigned tirelessly for Trump, has been another contender, but scrutiny over business dealings has raised questions that could disqualify him and his penchant for rhetoric may sit uneasily with becoming chief diplomat.

With senior cabinet nominations still pending, Trump and vice president-elect Mike Pence are scheduled to lead a post-election rally in Cincinnati, Ohio on Thursday. Trump was the first Republican nominee to win the state since 2004.

The evening event at the home of the Cincinnati Cyclones, with a maximum capacity of more than 17,000, is expected to be similar to those that drew enthusiastic crowds of thousands during the campaign.

The transition team has dubbed it a "thank you tour."

While such rallies are untraditional for a US president-elect, Trump often spoke of the thrill of addressing such enormous crowds during the campaign.