A poll testing how Josh Kraft, son of the New England Patriots’ billionaire owner, would fare against Mayor Michelle Wu in the 2025 election is circulating among Boston residents, the Herald has learned.

Multiple sources told the Herald that residents have been contacted this week with questions around whether certain aspects of Kraft’s candidacy, such as who his father is, his charity work, and his past support and donations to Republican politicians would be viewed favorably or unfavorably if he were to run for mayor.

While it’s unclear who is behind the poll — though one City Hall source interpreted the way the questions were framed as pointing to Kraft’s camp — the mere fact that such a survey is being conducted adds to the rumors that Kraft, head of the family’s philanthropic arm, is considering a run for mayor.

Two longtime political consultants who spoke to the Herald on background described the poll as a type of “message testing” that may be done by a candidate who is mulling a run for political office or re-election in Wu’s case, or an outside group or labor union looking to position a candidate or themselves in the race.

“I would think people are looking at focus groups,” Larry DiCara, a former city councilor and longtime observer of Boston politics, said on Tuesday. “I don’t know. I’m not involved, but if somebody’s serious about running for office, they should know the lay of the land — and especially if your name’s never been on the ballot, you don’t know where your strengths and your weaknesses are.”

Also prohibitive is the cost of a professional poll, which DiCara and political consultants put at roughly $30,000 to $50,000, which could point to candidates who can afford that hefty price tag, such as Kraft and the mayor.

Mayor Wu has yet to declare her plans to run for a second term, but has stated that it is very likely and continues to fundraise — her campaign war chest stands at more than $1.5 million.

While residents are broadly being asked who they would vote for if the 2025 mayoral election included Wu, Kraft, City Councilor Ed Flynn and North End restaurant owner Jorge Mendoza-Iturralde, the poll was “clearly designed” to portray it as a “two-person race” involving Wu and Kraft, a source whose family member received a phone call Monday night said.

Of the four, only Mendoza-Iturralde has declared his intention to run, but has yet to set up an account with the Office of Campaign and Political Finance. Flynn has been non-committal thus far, at first denying he was considering a run, but later saying that he was keeping his options open and would not rule it out.

Residents are being asked about Kraft’s past support for former Republican governor Charlie Baker and a lot of questions about his charity work, sources said about this week’s poll.

Pollsters also played up Kraft’s leadership stint at the Boys and Girls Club, as part of their effort to promote him as someone who has been involved in the community, according to the source whose family member received a call.

The questions were aimed at gauging what the support would be for Kraft, and testing his vulnerabilities, particularly the partisan vulnerability in a Democratic city of supporting and donating to Republicans.

Kraft’s father, New England Patriots owner Robert Kraft, who reportedly has a long-standing friendship with former President Donald Trump, the 2024 Republican presidential candidate, was also brought up by pollsters, a source said.

“Boston is a Democratic stronghold that becomes more progressive every single year,” Brian Jencunas, a Boston political consultant, said. “No matter what, Boston mayoral voters are going to be skeptical of a former Republican. If Donald Trump wins the 2024 election, that’s going to change from skepticism to immediate rejection, because Kraft will be held accountable for everything his erstwhile party is doing.”

Other questions centered around issues involving Wu’s potential vulnerabilities, such as the city’s open-air drug market at Mass and Cass, Boston Public Schools, and taxes, a source said.

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The mayor has faced criticism for the crowding and drug use that has returned to Mass and Cass this summer, the city’s struggling public school district and her failed attempt to move the O’Bryant school to West Roxbury, and her pending plan to raise commercial tax rates amid declining office property values.

DiCara and two political consultants who spoke with the Herald pointed to how difficult, and nearly impossible, it would be to unseat an incumbent mayor in Boston. The last time it happened was in 1949 when James Michael Curley lost his re-election bid to John B. Hynes.

One consultant, however, saw Wu as vulnerable to a potential candidate of color who’s willing to be “center-left” or one with name recognition and resources like Kraft, saying that the mayor has failed to build solid relationships and connections with the community members who did not help to put her into office.

That source pointed to some of the issues brought up by pollsters this week, the pushback Wu has received from communities of color over some of her proposals, particularly the O’Bryant move and her plan to renovate White Stadium to house a professional women’s soccer team, which led to a lawsuit by neighbors, and her more recent battle over the city budget with City Council leadership.

Others remained unconvinced.

“Mayor Wu certainly faces challenges from the decline in commercial property values, which will either lead to residential tax hikes or service cuts,” Jencunas said. “At the same time, Boston is the safest big city in America and property values continue to skyrocket. This is not the environment where an incumbent Boston mayor loses for the first time since 1949.”

Mayor Michelle Wu (Nancy Lane/Boston Herald, File)