"It seems to me she's got the experience. She's got the temperament for it. I think she would be well received around the world," said Sen. Jon Kyl, R-Ariz. "So my own initial reaction is it would be a very good selection."
Both Clinton, Obama's fiercest rival for the presidential nomination, and New Mexico Gov. Bill Richardson, who also ran for the White House this year, interviewed with Obama in Chicago last week for the post, according to Democratic officials.
Sen. Byron Dorgan, D-N.D., said he did not think Clinton, if nominated, would have trouble winning confirmation in the Democratic-controlled Senate.
"She's worked across the aisle, has good bipartisan relationships," Dorgan said. In the role of chief U.S. diplomat, Clinton "would have instant credibility around the world," he added.
He said the U.S. has "a lot of relationships to repair and a lot of work to do, so I think she'd be a fine choice."
Richardson has extensive foreign policy experience. He was President Bill Clinton's ambassador to the United Nations and has conducted freelance diplomacy for the U.S. in Sudan, North Korea and elsewhere.
Richardson and Clinton are not the only candidates Obama has talked to about the job, Democrats said.
Kyl and Dorgan appeared on "FOX News Sunday."