And without Mr. Trump’s direct intervention, Ms. Blackburn is highly unlikely to bow to Mr. Corker.
“Marsha Blackburn is not getting out of this race regardless of who gets in,” said Ward Baker, the Nashville-area lawmaker’s chief strategist.
Further, Senator Mitch McConnell of Kentucky, the majority leader, has rebuffed Mr. Corker by telling him that he must secure the president’s support to re-enter the race, according to Republicans familiar with the conversation, a rare act of political deference that suggests he is uneasy about driving Ms. Blackburn out of the primary race.
But Mr. Corker and some of his Senate allies are aggressively working to win over the White House, embarking on what one West Wing official described as a sudden charm offensive. The senator has avoided any criticism of Mr. Trump in recent weeks and on Monday met with Ivanka Trump, the president’s daughter.
Mr. Trump’s political advisers, getting wind of the meeting, scrambled to brief Ms. Trump and her own staff about Mr. Corker’s renewed interest in running again and his desire for the president’s support, according to a Republican official. An aide to Mr. Corker said Ms. Trump requested the meeting.
More broadly, Mr. Corker’s advisers say he and Mr. Trump have patched up their relationship and the senator is simply hearing out those who would like him to remain in the Senate, a decision he technically does not have to make until Tennessee’s filing deadline in early April.
“In recent days, people across Tennessee have reached out to Senator Corker with concerns about the outcome of this election because they believe it could determine control of the Senate and the future of our agenda,” said Micah Johnson, Mr. Corker’s spokeswoman.
Mr. Corker is not the only Republican who could shake up a closely watched Senate race. Representative Kevin Cramer of North Dakota, who had been heavily courted by Mr. Trump and other leading Republicans but decided against a bid, is now signaling that he may mount a bid after all against Senator Heidi Heitkamp, North Dakota’s freshman Democrat.
If Mr. Cramer’s potential change of heart is lifting Republicans’ spirits, the party is now uneasy about the prospect of having one too many Republicans in Tennessee.
Mr. Corker’s hopes for a rapprochement with Mr. Trump illustrate the degree to which loyalty to the president is becoming a central litmus test in Republican politics. And that he might consider a reconciliation with a senator who only a few months ago portrayed him as an unruly toddler underscores that there are no permanent friends or enemies to Mr. Trump.
But party officials overseeing the midterms have little appetite for a bloody primary campaign in Tennessee.
Democrats have cleared their field for Phil Bredesen, a wealthy former two-term governor and mayor of Nashville whose prospects in an increasingly conservative state would markedly improve if he faced a Republican limping into a general election.
Further, in a season full of disappointments across the Senate Republican map, Ms. Blackburn has been a bright spot, raising $2 million in the final quarter of last year, contributing to other candidates and uniting most of the party’s factions.
“She is raising more money and doing more than any other candidate in country,” said Josh Holmes, a Republican consultant and adviser to Mr. McConnell.
Ms. Blackburn, who was already facing former Representative Stephen Fincher in the primary, is signaling that if she is forced to take on Mr. Corker she will wield her gender as a political weapon. That would raise a delicate issue for a Senate Republican caucus that includes just five women in its ranks.
“Anyone who thinks Marsha Blackburn can’t win a general election is just a plain sexist pig,” said Andrea Bozek, a spokeswoman for Ms. Blackburn, adding, “We aren’t worried about these ego-driven, tired old men.”
That is an unmistakable reference to a bloc of establishment-aligned Tennessee Republicans who believe Ms. Blackburn’s conservative politics and hard-charging style may turn off some voters and make her vulnerable against the centrist and low-key Mr. Bredesen.
Tom Ingram, a Republican strategist and a longtime friend of Mr. Corker’s, argued that Republicans could imperil the seat and their one-seat majority if they do not rally around an incumbent who has already won the state twice.
“It’s a dicey race with an unproven statewide candidate against Phil Bredesen,” Mr. Ingram said. “If Corker is the nominee, it’s not in play.”
Fueling the anxieties of some Tennessee Republicans is the openness some in the party’s donor wing have toward backing Mr. Bredesen. Concerns about such defections cropped up again this week when an invitation to a $5,400-per-couple Bredesen fund-raiser hosted by the widow of the former Nashville Republican powerhouse Ted Welch began circulating among Republicans.
Such talk induces eye-rolling among a younger generation of Republicans in Tennessee.
“Every Republican in Tennessee outside the walls of the Belle Meade Country Club believes Marsha is a heavy favorite against anybody who might get in that primary,” said Brad Todd, a Republican consultant raised in the state who is not aligned in the Senate race.