On Monday, at a fund-raising event in Manhattan for the New York State Republican Party, David Koch told donors that he and his brother, who oversee one of the biggest private political organizations in the country, believed that Mr. Walker would be the Republican nominee.
"When the primaries are over and Scott Walker gets the nomination," Mr. Koch told the crowd, the billionaire brothers would support him, according to a spokeswoman. The remark drew laughter and applause from the audience of fellow donors and Republican activists, who had come to hear Mr. Walker speak earlier at the event, held at the Union League Club.
Two people who attended the event said they heard Mr. Koch go even further, indicating that Mr. Walker should be the Republican nominee. A spokeswoman disputed that wording, saying that Mr. Koch had pledged to remain officially neutral during the primary campaign.
But Mr. Koch's remark left little doubt among attendees of where his heart is, and could effectively end one of the most closely watched contests in the "invisible primary," a period where candidates crisscross the country seeking not the support of voters but the blessing of their party's biggest donors and fund-raisers.
Few donors have been courted as aggressively as the Kochs, whose network of political nonprofits, "super PACs" and like-minded donors plans to spend almost $900 million over the next two years advancing conservative candidates and policies.
Republican presidential contenders including Senator Ted Cruz of Texas and Gov. Chris Christie of New Jersey have sought out the men for private meetings in Wichita, Kan., and New York, joined them for rounds of golf, and sought coveted invitations to the brothers' annual donor conference in Southern California. Senator Rand Paul of Kentucky wrote an opinion article for Time Magazine's "100 Most Influential People" issue last week, praising the two men for their "passion for freedom and their commitment to ideas."
But the ultimate value of the Kochs' good will in a Republican primary is difficult to measure.
Mr. Koch's remarks suggested that the political organizations they oversee — which include Americans for Prosperity, a grass-roots organization, and Freedom Partners, a donor trade group with an affiliated "super PAC" — would not intervene in the Republican primary process on behalf of a single candidate.
But according to the two attendees, who spoke on the condition of anonymity to freely describe the remarks, Mr. Koch suggested that the Koch family might personally offer financial support to Mr. Walker.
In a statement, Mr. Koch described the Wisconsin governor as "terrific," but said he was not making an endorsement.
"Let me be clear, I am not endorsing or supporting any candidate for president at this point in time," Mr. Koch said.