Singer Jennifer Lopez and former New York Yankees baseball star Alex Rodriguez said Saturday they were "working through some things", but called reports they had broken up "inaccurate".

Celebrity news website TMZ, the New York Post's Page Six and other US media sources reported on Friday that the couple had broken off their engagement.

"All the reports are inaccurate. We are working through some things," they said in a joint statement to US media.

Lopez, 51, and Rodriguez, 45, became a couple nearly four years ago and had just last year bought a $40 million home in Miami.

Rodriguez posted a selfie to social media on Friday of himself aboard a boat in Miami.

"Don't mind me, just taking a sail-fie," he wrote. "What are your plans for the weekend?"

Lopez was in the Dominican Republic filming a movie and posted Thursday on social media saying "Find a good reason to laugh today."

"They hit a rough patch. But were not broken up," a source close to the pair told People magazine.

"She's working in the Dominican Republic and he's in Miami so it's tough seeing each other," the source added.