Still, Hatch said, "that's going to be up to her what she does."
Kagan addressed the issue of recusing herself from the health care law decision during her confirmation hearing before the Senate Judiciary Committee, as GOP senators pressed her on how much involvement she had in the White House's push for the legislation.
Kagan said she was never asked for her opinion on the merits of litigation challenging the law.
"I attended at least one meeting where the existence of the litigation was briefly mentioned," Kagan said, "but none where any substantive discussion of the litigation occurred."
In written testimony to the committee before the hearings, Kagan simply responded "no" to questions about whether she had been asked her opinion, offered advice or discussed the legal and constitutional merits of the health care law.
On Thursday, Hatch was more circumspect in what Kagan should do. The Utah Republican told The Salt Lake Tribune he was just raising the issue of whether Kagan should consider taking herself out of any health care reform appeal but that she has sole authority to do so.
"I don't have direct knowledge of what she did or did not do," with regard to working on health care, Hatch said. "I raise it as an issue that certainly has to be considered."
Kagan is the most recent addition to the nine-member Supreme Court and is viewed as standing with the bench's more liberal members.
Sidelining her probably would boost the health care reform critics' case to the high court.
Two federal judges have ruled in favor of lawsuits brought against the constitutionality of the health care reform law, while other judges have done just the opposite.
The Supreme Court ultimately could decide the issue.