WASHINGTON — President Obama is vetting Jane L. Kelly, a federal appellate judge in Iowa, as a potential nominee for the Supreme Court, weighing a selection that could pose an awkward dilemma for her home-state senator Charles E. Grassley, who has pledged to block the president from filling the vacancy.

The F.B.I. has been conducting background interviews on Judge Kelly, 51, according to a person with knowledge of the process. The person spoke on the condition of anonymity because the White House is closely guarding details about Mr. Obama’s search to fill the opening created by the death of Justice Antonin Scalia.

The president is expected to make his selection in the next couple of weeks, a decision that could reshape the court for decades but faces heated opposition from Republicans in Congress.

Mr. Grassley is at the center of that fight as the chairman of the Senate Judiciary Committee, a post in which he alone can decide whether to hold confirmation hearings on a nominee. Like the panel’s other Republicans, he has vowed not to take any action until after the November election, arguing that the choice should be left to the next president.