Citing a source who it said was at the meeting Monday in Des Moines, the U.S. news network said the group is seeking a consensus candidate.
Many members of the Christian Right distrust Romney because they believe he was soft on issues such as abortion and gay marriage while governor of Massachusetts. There has been much speculation among political pundits online and cable TV that Romney's Mormon faith is problematic for many Christian evangelicals.
The Iowa caucuses are scheduled Jan. 3.
Romney has led in polls of Republican voters but seems stuck at just under 25 percent, while other candidates -- such as Minnesota Rep. Michele Bachmann, Texas Gov. Rick Perry and former corporate executive Herman Cain of Georgia -- have shot up and then faded. Former House speaker Newt Gingrich is the latest to push Romney in the polls.
CNN's source was pessimistic about the effort to find an alternative to Romney.
"Somebody who's at 5 percent or 6 percent in the polls, and they endorse, I don't think that does any good," the source told CNN.
Notable deaths of 2014 [PHOTOS]