Last week, reports indicated that the 51-year-old multihyphenate and former baseball pro, 45, had ended their engagement after several years together.
Not long after, the two offered a statement to Fox News that said, "All the reports are inaccurate."
"We are working through some things," the statement continued.
Just days ago, it was reported that Rodriguez had flown to the Dominican Republic, where Lopez is currently filming a movie.
In photos obtained by Daily Mail, the pair could be seen sharing a smooch outdoors while the actress lounged in a white bathrobe.
In other photos, Lopez appears to happily greet Rodriguez upon his arrival and even wraps her arm around him as he kneels down to her level.
A source also recently told People magazine that Lopez "was excited to see" Rodriguez "in person" ahead of their DR reunion.
"They are really trying to figure things out," the source added. "It was a happy reunion."
On Monday, Rodriguez wrote on his Instagram Story, "New week. New day. Onward. Upward," as he panned a tropical landscape and tagged Lopez.
A source further claimed to Fox News that, while reports of their breakup were premature, the two have recently run into some issues.
"Nothing was concrete. They hit a rough patch but are working through it," the source said.
An initial report from Page Six claimed Lopez was busy in the Dominican Republic filming a movie while Rodriguez is "in Miami getting ready for baseball season."
Recent reports also pointed to previous rumors stemming from earlier this year regarding an alleged romance between Rodriguez and "Southern Charm" star Madison LeCroy. Multiple sources indicated at the time that there was no connection between the two, however.
A source claimed to Fox News on Saturday that a third party "did not contribute" to the couple's recent troubles.
"Jennifer and Alex have much bigger things -- like businesses and their [respective] kids -- to worry about," the source claimed.
Fox News' Jessica Napoli and Melissa Roberto contributed to this report