Alina Habba, who has used her job as New Jersey’s top federal prosecutor to aggressively target Democrats, is pursuing an investigation into remarks made by Gov. Philip D. Murphy about housing a migrant, according to three people with knowledge of the matter.

Mr. Murphy said in February that he was prepared to house a woman whose immigration status was unclear at his family’s home in Middletown. F.B.I. agents have since sought to interview at least four witnesses in connection with the comments, two of the people said, with one adding that the governor had been subpoenaed but not questioned.

Ms. Habba, the interim U.S. attorney in New Jersey, is a former personal lawyer for President Trump. She previously announced that she was directing prosecutors in her office to investigate the governor and New Jersey’s attorney general, Matthew J. Platkin, in connection with the state’s immigration policies.

Two of the people with knowledge of the investigation involving Mr. Murphy’s comments indicated that it was separate from any Justice Department inquiry related to New Jersey’s so-called sanctuary policy, which has been upheld by a federal appeals court. There has been no public sign of that inquiry moving forward.

Mr. Murphy is one of at least four Democratic officials to become entangled in investigations pursued by Ms. Habba since she was named to the position in late March.

Mr. Murphy made the remarks during a freewheeling discussion at a New Jersey college, telling an audience there that there was a person in his social orbit “whose immigration status is not yet at the point that they are trying to get it to.”