Lopez and Smart have been dating for nearly two years but it is being said that they have been fighting a lot recently, reported E! News.
"Things are not going well at the moment. They are bickering and it's clear to the people around them that there is an irritation between them at the moment. It's hot and cold, but more cold than hot right now," a source said.
The thrice-divorced mother of two and her choreographer beau reportedly "never thought it was going to be long-term."
Lopez separated from third husband Marc Anthony in July 2011.
Lopez is currently judging the reality show American Idol. The couple was last photographed out in public on September 21.