As President Trump gets a jump on 2020 by rolling out his hand-picked re-election team, he’s already facing rumblings of a possible Republican primary challenge.

Outgoing Arizona GOP Sen. Jeff Flake, an outspoken Trump nemesis, plans next month to visit early-voting state New Hampshire to speak at the high-profile “Politics and Eggs” event.

A candidate’s performance in the state’s primary, which historically follows the first-in-the nation Iowa caucuses, is seen as a critical test in the nomination battle.

Flake said last year he wasn't planning to run, but didn't rule it out either. Flake’s office confirmed the New Hampshire trip to Fox News on Tuesday -- and the appearance immediately revived speculation about his intentions.

On the same day, Trump named former digital adviser Brad Parscale as his 2020 campaign manager and announced other top re-election campaign officials.

Trump -- who, with Parscale's help, made the once-unthinktable jump from real estate and reality TV magnate to president-elect in 2016 -- says Parscale will lead “advanced planning” for the 2020 effort.

The announcement was yet another step toward Trump’s re-election effort. He already filed paperwork to organize his 2020 committee, held his first campaign rally in February 2017 and continues to make pre-emptive jabs at any potential 2020 challengers -- most recently Oprah Winfrey, a strong Democratic Party supporter who now says she won't run.

Flake did not endorse Trump’s 2016 presidential campaign and has remained a prominent critic, most recently suggesting his attacks on the media are Stalin-esque.

His opposition to Trump, and the backlash in a state that gave Trump 49 percent of the 2016 vote, likely contributed to Flake’s decision not to seek a second term.

Trump has, in turn, attacked Flake a handful of times on Twitter, calling him “weak” and “toxic.”

Beyond Flake, Ohio Gov. John Kasich also may be considering another White House bid, after losing to Trump in the 2016 GOP presidential primary.

Like Flake, Kasich has been highly critical of the president. However, their rivalry, at least for now, has calmed. Kasich even said Trump “deserves credit” for seeking a ban on so-called bump stocks, which enable rifles to fire rapidly, in the aftermath of the Feb. 14 mass shooting at a Parkland, Fla., high school.

Kasich has said he’s not interested in another White House bid, which in 2016 he waged deep into the campaign season despite having little money and long odds for success.

Still, the outgoing governor and his advisers are considering whether to again challenge Trump in the GOP primary or mount an independent party bid, according to Politico.

He also plans to attend the same New Hampshire event this spring and has remained in the national spotlight, with frequent TV appearances and a book tour.

Flake is planning to visit New Hampshire on March 16. The annual event is hosted by Saint Anselm College's New Hampshire Institute of Politics. A Flake spokesman said the senator is working on a speech for the event titled, "Country Over Party."

Another possible 2020 GOP challenger is Dallas Mavericks owner Mark Cuban, who told Fox News last fall that if he ran for president, he would be a Republican candidate.

The outspoken Cuban, whose name is frequently mentioned in speculation about potential presidential candidates, was an early 2016 Trump supporter -- then became a sharp critic and backer of Democratic nominee Hillary Clinton.

Fox News’ Mike Emanuel and Nicholas Kalman and The Associated Press contributed to this report.