The engagement story emerged after she showed off a massive diamond rock on the ring finger of her left hand when attending Paris Fashion Week earlier this week.
Lopez flashed the jewelery when attending a showcase for Chanel Spring/Summer 2013 collection with Smart and her daughter Emme, reported Aceshowbiz.
"She's in the middle of her tour and her manager doesn't want her distracted. He wants her to focus, and an engagement would distract her too much," a source said.
Even if the ring was a gift from Smart, the source says that the couple was not going to swap vows anytime soon.
"This ring could just be for their anniversary," the source added.
