Senate Minority Leader Mitch McConnell said Kerry, chairman of the chamber's Foreign Relations Committee, would be a "popular choice with the Senate," CNN reported Friday.
Rice, the U.S. ambassador to the United Nations, withdrew from consideration for the post Thursday, saying she didn't want a drawn-out, polarizing nomination process because of remarks she made days after the attack on the U.S. Consulate in Benghazi, Libya, in which Ambassador Christopher Stevens and three other diplomatic employees died.
In the initial interviews following the Sept 11 attack, Rice called the violence part of "a spontaneous reaction" against an U.S.-produced anti-Islam video. Reports later indicated the violence resulted from a planned terrorist attack. Republicans suggested Rice intentionally misled the public to shield President Obama politically in the final weeks of the presidential campaign.
"I don't regret doing it," Rice told NBC News. "When you're a diplomat and a public official and a tragedy happens and it related to the work we do, it's our obligation to explain it as best we can to the American people."
Kerry, who was attacked over his war record by Republicans and GOP-supporting allies during his 2004 presidential run, recalled that experience in a statement about Rice, CNN said.
"As someone who has weathered my share of political attacks and understands on a personal level just how difficult politics can be, I've felt for her throughout these last difficult weeks, but I also know that she will continue to serve with great passion and distinction," Kerry said.
In her interview with NBC News, Rice said she didn't want a polarized and politicized nomination process "because there are so many things we need to get done as a country, and the first several months of a second-term president's agenda is really the opportunity to get the crucial things done."