(CNN) — The under-the-radar race to replace Mitch McConnell is a wide-open affair with no clear front-runner, according to many GOP senators, as the top contenders begin jockeying to win over their colleagues for a position central to their party’s agenda and strategy.

The election to succeed McConnell – the longest-serving Senate party leader in history who has dominated his conference for nearly two decades – is expected to slowly play out from now until after the November elections when the secret-ballot race officially takes place. And in the immediate aftermath of McConnell’s announcement, the candidates had already begun one-on-one outreach with individual members, as they plan to lay out their strategy and agenda and try to secure commitments of support along the way.

“I’ve had a lot of calls from people today,” said Sen. Susan Collins, a Republican from Maine, who has not committed to a candidate yet.

And some said that the jockeying had begun months ago – since it had been long expected McConnell would step aside at the end of the year, though the timing of his announcement was never certain.

“Oh, that started a long time ago,” said Sen. Mike Rounds, the Republican who is backing Senate GOP Whip John Thune – his fellow South Dakotan – for the spot.

Two of the top three candidates for the post, known as the “three Johns” — Thune, Senate Republican Conference Chairman John Barrasso of Wyoming and Sen. John Cornyn of Texas, a former whip — have yet to formally declare their candidacies but are expected to run. Cornyn announced Thursday his plan to run for Senate GOP leader and said that he spoke to Trump about his intentions.

“I’ve had a couple of good conversations with him most recently yesterday, telling him my intention, told him that I had worked with him when I was the majority whip for four years and worked very successfully, in my opinion, with him and his team, and I look forward to doing that again,” Cornyn said.

Asked if Trump was supportive of his bid, Cornyn said, “He wanted to know who was interested who was running, so we didn’t have that conversation.”

Other candidates could yet emerge. And it’s entirely possible, the candidates could shift their strategies. Barrasso, for one, could ultimately decide to move one spot up and run for whip, the No. 2 position, though he has yet to make his intentions known.

The shakeup within the Senate GOP ranks comes as the conference has grown increasingly divided between its Trump and establishment wings. And how Thune, Cornyn and Barrasso placate the various factions within the conference — and make promises to elevate their rank-and-file in the decision-making process — could help determine whether they have the votes to be leader.

“I’m going to talk to members of my conference, hear what they have to say, listen to them in terms of what direction they want to take with the conference,” Barrasso told reporters.

One major question: How the next leader will deal with former President Donald Trump — especially if he wins the presidency. Each of the three men have had their own approaches to Trump, with Thune maintaining the rockiest relations with the former president of the three.

It wasn’t until this past weekend that Thune endorsed Trump, following Barrasso – who was first – and later Cornyn. Thune said he didn’t know if it would make much of a difference to senators.

“I don’t think so,” Thune told CNN. “What role that plays, I don’t know. These are elections that are largely secret ballots so I don’t know.”

But they have had their differences on policy from time-to-time. Thune and Cornyn voted for the $95.3 billion aid package for Ukraine, Israel and Taiwan – while Barrasso opposed it.

Thune may have a leg-up in some quarters — since he is the current No. 2 and viewed by some Republicans as the heir apparent.

Indeed, in many ways, McConnell did Thune a favor by bowing out early. Had McConnell stayed as leader through the next Congress, there would be a new whip in 2025 – potentially Barrasso – since Thune is term-limited from the No. 2 position at the end of the year.

“He’s done a nice job navigating the system,” said Sen. Markwayne Mullin of Oklahoma, who is backing Thune for the job and believes the South Dakotan is the front-runner. Mullin said of Thune: “I thought he did good when Mitch was having medical issues,” referring to when McConnell was out for nearly six weeks last year after suffering a concussion and broken ribs from a fall.

While both Thune and Barrasso were both quick to win support from the junior GOP senators in their state delegations, that doesn’t yet apply to Cornyn. His junior senator – Ted Cruz – would only say, “There’ll be plenty of time for the conference to make those decisions” when asked about supporting Cornyn.

In his announcement Thursday, Cornyn cited his relationship to Trump and described the Senate as “broken.”

“The good news is that it can be fixed, and I intend to play a major role in fixing it,” Cornyn said, adding promises to restore regular order to the funding process and “no more backroom deals or forced votes on bills without adequate time review, debate, and amendment.”

Others said they would wait to decide which senator to back after hearing how the candidates will address their concerns.

“I want to get good answers to the questions,” said Sen. Kevin Cramer, a North Dakota Republican. “My concerns are mainly about the functionality of this place.”

There also could be pushes by hard-right senators who are strong backers of Trump to install a more like-minded candidate for leader, especially if Trump wins back the White House.

”I think it’s pretty clear Donald Trump is the largest force in the Republican Party,” said Sen. Lindsey Graham, a Republican from South Carolina and loyal Trump ally. “There is no mystery there … I think we’ll be in the majority, and I think Trump will be president – will have to be somebody who can work with Trump, but also all factions of the party.”

Many said it was hard to gauge who would have a leg-up.

“Who knows,” Oklahoma Sen. James Lankford said when asked which candidate he would back. “At this point I don’t have a pick on it, and there’s going to be 48 other people looking at it. I’m not one of those by the way, but there will be others that will look at it and we’ll see where it goes.”

Utah Republican Sen. Mike Lee, a staunch conservative and leading McConnell critic, said he is not ruling out running for the job, but said he’s more interested in hearing from the candidates about where they want to take the conference. Lee would be considered a long-shot candidate.

“I am very good friends with all three of them,” he said. “The specific person is far less important to me than what their strategy is, and I need to hear from them on what ideas they’ve got.”

Others are pressing the candidates to make specific commitments.

“We’re starting to have conversations,” said Sen. Ron Johnson, a Wisconsin Republican and vocal McConnell critic. He wants to come up with a “mission statement” for the conference and make up his mind based on whether the candidates support that statement.

“I’d say I think what the Republican Conference in the Senate ought to do is we need to be the counter to the radical left agenda that’s destroying this country,” Johnson said.

Many Republicans said there was plenty of time to sort out their future leader.

“I plan to support John,” Sen. JD Vance of Ohio quipped.

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