Jennifer Lopez and Alex Rodriguez Reportedly Couldn't Handle Long Distance Relationship

Jennifer Lopez and Alex Rodriguez are still together, but their relationship ran into some trouble when Lopez left the U.S. to start working on her next movie, Shotgun Wedding, in the Dominican Republic. On Friday, sources told multiple outlets that the couple broke up, but they quickly shut down those reports on Saturday and said they are "working through some things." Rodriguez, 45, also told photographers outside his Miami gym Saturday that he is not back on the market.

Late Saturday, a source told PEOPLE the couple started "having problems" before Lopez, 51, left for the Dominican Republic, but the trip exacerbated the situation. "Filming made it worse because they haven't been able to see each other in person," the source explained. "But they love each other and want to keep working on things."

Speculation about the couple experiencing a rough patch started in February when Southern Charm star Madison LeCroy admitted she did communicate with Rodriguez but said they never had a physical relationship. An insider told PEOPLE this situation had "no bearing" on their issues though. "This was not caused by a third party. Madison [LeCroy] or anyone else," one source said. "They are working through things."

"She's working in the Dominican Republic and he's in Miami so it's tough seeing each other especially with quarantining and COVID," another insider told PEOPLE. "But they want to try to stay together."

Lopez and Rodriguez got engaged in 2019 during a trip to the Bahamas after two years of dating. Rodrigez and ex-wife Cynthia Scurtis are parents to daughters Ella, 12, and Natasha, 16. Lopez and ex-husband Marc Anthony are parents to 13-year-old twins Maximilian and Emme. The couple delayed their wedding twice last year due to the coronavirus pandemic. In a January interview with Elle, Lopez said the two were not in a rush to tie the knot.

"We postponed the wedding twice. We had planned what we really, really wanted to do, [but] I don't know if we'll be able to re-create that. We canceled it, and since then we haven't really talked about it. There's no rush. We want to do it right when we can do it," Lopez told Elle. "We just have to wait to see where the world lands." Lopez also told Allure in February that they did therapy sessions that were "really helpful" for their relationship.