Following the surprise announcement earlier in the week that Senate Republican Leader Mitch McConnell (R-KY) would step down from that leadership role after the November elections, a scramble has ensued for who will be his successor in that top spot.

Multiple reports indicate that former President Donald Trump has reached out to encourage a leadership run by his preferred replacement for McConnell, Sen. Steve Daines (R-MT), who has confirmed that outreach but won't say definitively if he will make that run or not, the Daily Beast reported.

To be the next Senate GOP leader, Daines would likely need to leapfrog the so-called "Three Johns" who are already aligned in leadership roles behind the outgoing McConnell, including Sens. John Thune (R-SD), John Cornyn (R-TX), who has already announced a likely leadership bid, and John Barrasso (R-WY), who has also earned a favorable mention from Trump as an acceptable McConnell replacement.

Daines confirmed outreach from Trump

Politico reported Thursday that Sen. Daines, who currently chairs the National Republican Senatorial Committee, confirmed to reporters that former President Trump had reached out to him and "thanked" him for his encouragement but declined to say for sure if he would run for the top spot or not.

Instead, the Montana senator revealed that "I told [Trump] the most important thing I can do this moment is to make sure we have a Senate majority in November."

The outlet noted that Daines and Trump have been quietly working together to make strategic picks and endorsements of candidates that can win both primary contests and the general election in this particular cycle that arguably offers Republicans their most promising opportunity to flip several Democrat-held seats and regain majority control of the Senate.

If not Daines, then Barrasso

Axios similarly reported that former President Trump had reached out to Sen. Daines as his preferred pick to succeed Sen. McConnell as the Senate Republican leader but noted that the outreach actually began before McConnell made his surprising announcement that he would soon vacate the leadership position he's held with little or no opposition since 2007.

One unnamed source described as "familiar" with Daines' thinking on the matter said the Montana Republican "appreciates the president's support but needs to focus on taking back the Senate" in November's elections.

The outlet noted that if Daines opts not to make a bid for the leadership spot once McConnell has stepped aside, Trump's second choice for that position would be Sen. Barrasso.

Cornyn already announced a leadership bid

The Daily Beast observed that Sen. Thune, as the current No. 2 to Sen. McConnell, would seemingly hold the frontrunner status to be the replacement, though Sen. Cornyn, who previously held that No. 2 slot, has already indicated his intention to make a run to be McConnell's successor.

"From experience, I have learned what works in the Senate and what does not," the Texas senator reportedly said in an internal message sent to his GOP colleagues. "And I am confident Senate Republicans can restore our institution to the essential role it serves in our constitutional republic."

The outlet noted that while all three of the "Three Johns" have endorsed former President Trump as the likely Republican nominee, Thune and Cornyn have previously been rather critical of Trump and are most closely aligned with the D.C. establishment while Barrasso has been the most friendly with and receptive toward the former president over the years.

Trump's influence on Senate leadership could be limited by secret ballot, his own race for re-election

Axios reported that if Sen. Daines is successful in helping Senate Republicans reclaim majority control in November, he would likely position himself as the leading contender to replace Sen. McConnell as the party's leader in the upper legislative chamber going forward.

Unlike in the House, where the leadership battles are largely conducted out in the open, Senate leadership is chosen behind closed doors with secret ballots, and while that could serve to limit the extent of former President Trump's influence on the process, per Politico, it stands to reason that he will still hold substantial sway over that process, especially if he wins his own bid for re-election in November.