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Dan Farber, another Berkeley constitutional law professor, said there was no conflict when Mr. Bush signed the order earlier this year.

“The last thing he had in mind was that he could sway Clinton’s vote by promising her the position with higher pay, and any possible conflict is eliminated if she doesn’t actually get the higher salary,” he said.

Paul Orfanedes, director of litigation for Judicial Watch, said the group was looking for someone who could have standing to sue based on the clause, such as a State Department employee.

“If we could find someone, it looked like a good solid legal case,” he said. “Sure.”

For her part, Mrs. Clinton has not commented on the complaint.

Mr. Obama is expected to name Mr. Richardson to the post at a 10:40 a.m. EST press conference in Chicago. On Tuesday, the president-elect and named Louis Caldera to serve as director of the White House Military Office.

c Nicholas Kralev contributed to this report