Lopez and Anthony, who wed four years ago and are the parents of 10-month-old twins, have been attending functions solo and aren't wearing their wedding rings, Us magazine reported on its Web site.
"They both didn't wear their rings on purpose," Us quoted a friend as saying. "Nothing Jennifer does is without purpose."
The two are also said to have had a tense Thanksgiving in which they didn't sit together and barely spoke to each other.
Friends claim Anthony is controlling and that Lopez blames him for her career taking a nosedive.
"Jennifer looked around and said, 'This is my life now? I'm a Long Island housewife?'" a source close to Lopez told the magazine. "She hates that everything she worked for went down the tubes."
Anthony's publicist maintains, however, that the couple is doing fine, Us said.