WASHINGTON — As the Republican Party looks toward the next cycle of gubernatorial races, few contests have generated as much quiet anxiety within party ranks as Minnesota, where the political ambitions of Mike Lindell have become a source of unease — and where the influence of Donald Trump looms large.

Mr. Lindell, the founder of MyPillow and one of Mr. Trump’s most loyal allies since the 2020 election, has announced his intention to seek the Republican nomination for governor. His candidacy, built largely around persistent claims of widespread election fraud, has alarmed many Republican strategists who fear it could all but guarantee a Democratic victory in a state the party has long struggled to reclaim.

Behind the scenes, senior Republicans describe a familiar dilemma: how to distance themselves from a controversial figure without alienating Mr. Trump, whose endorsement still carries significant weight among primary voters.

“Privately, there is real concern,” said one Minnesota-based Republican strategist, who requested anonymity to speak candidly. “Publicly, few are willing to say it.”

Mr. Lindell rose to national prominence not only as a businessman but as a tireless promoter of false claims that the 2020 presidential election was stolen. He financed lawsuits, documentaries and media campaigns alleging manipulation of voting machines — efforts that failed repeatedly in court and have since led to significant legal and financial consequences.

In recent months, Mr. Lindell has acknowledged severe business setbacks. MyPillow has lost major retail partners, faced eviction proceedings over unpaid rent and been embroiled in defamation litigation related to its election claims. Former legal advisers have publicly stated that they severed ties over unpaid fees. Yet none of this has appeared to dampen his political ambitions.

Nor has it weakened his relationship with Mr. Trump, who has repeatedly praised Mr. Lindell’s loyalty and echoed his claims about election fraud. For many Republicans, that loyalty is precisely the problem.

According to reporting by Politico, Republican officials in Minnesota worry that a Lindell nomination would transform the race into a referendum on Mr. Trump rather than on state-level issues such as taxes, public safety or education.

“If Lindell is the nominee, that’s what the election becomes,” said a former Republican speaker of the Minnesota House, warning that it would make the contest easier for Democrats to nationalize. “There’s no question.”

That prospect concerns party leaders who believe they would otherwise have a competitive chance against the incumbent governor, Tim Walz, a Democrat seeking another term. While Mr. Walz has faced criticism from conservatives over pandemic policies and spending priorities, he has also maintained relatively strong approval ratings in a state that has not voted for a Republican presidential candidate since 1972.

The fear, several Republicans say, is that Mr. Trump’s involvement — particularly if he actively campaigns for Mr. Lindell — would energize Democratic voters and repel moderates in suburban districts that have trended away from the party in recent cycles.

“When the former president comes in with inflammatory rhetoric, it leaves no room for nuance,” said a former Minnesota GOP official. “Everything gets pulled into his orbit.”

Mr. Trump, for his part, has shown little inclination to recalibrate his approach. Throughout his political career, he has rewarded personal loyalty above ideological consistency or electoral pragmatism. Allies who echo his grievances often receive public praise, while skeptics risk becoming targets of criticism.

That pattern has reshaped Republican primaries nationwide, elevating candidates with strong ties to Mr. Trump even when party leaders worry about their viability in general elections. In Minnesota, where statewide races are often decided by narrow margins, those concerns are particularly acute.

Mr. Lindell has dismissed criticism from within his party, arguing that his willingness to challenge election systems makes him uniquely qualified to lead. He has framed legal scrutiny of his businesses and activism as political retaliation, a narrative that resonates with a segment of the Republican base.

Still, some Republicans privately concede that the strategy carries high risk. “We should be competing on ideas and governing records,” one strategist said. “Instead, we’re relitigating 2020.”

Whether Mr. Lindell ultimately secures the nomination remains uncertain. But the debate surrounding his candidacy underscores a broader tension within the Republican Party: the struggle to balance loyalty to Mr. Trump with the practical demands of winning elections in competitive states.

In Minnesota, at least, that balance appears increasingly difficult to maintain — and the outcome may offer an early signal of how much influence Mr. Trump continues to wield over the party’s future.