On March 12, stories emerged that the couple had split, with one report saying their relationship had been "on the rocks."
"All the reports are inaccurate," the couple told TMZ in a joint statement. "We are working through some things."
A source also later said the two had never officially broken up, but had discussed it: "She's working in the Dominican Republic and he's in Miami, so it's tough seeing each other, especially with quarantining and COVID, but they want to try to stay together."
The couple's joint statement comes after J.Lo posted a video of her daughter, Emme, crying while sitting with her father, singer Marc Anthony, as the two spoke to Jennifer on FaceTime.
"When they are sad, but momma and daddy are their coconuts," J.Lo wrote in the Instagram Stories post.
The singer and actress is currently in the Dominican Republic working on a movie, while A-Rod is still in Miami. He posted a selfie on a boat in the Florida city on March 12, writing, "Don't mind me, just taking a sail-fie... What are your plans for the weekend?"
Jennifer and Alex started dating in 2017, and got engaged two years ago. The couple both have children from their previous marriages. Jennifer is mother to 13-year-old twins Max and Emme, from her relationship with Marc, while Alex has daughters Natasha, 16, and Ella, 12, from his marriage to Cynthia Scurtis. The stars had no problem blending their families, with their children quickly bonding after they moved in together.
The couple also own several properties together, including a US$40 million home they purchased last year on Star Island, a private island near Miami.
Last year, the couple postponed their wedding twice due to COVID-19. They had initially planned to marry in a ceremony in Italy in June, but social distancing and travel restrictions scuppered that.
Jennifer has been married three times before, having wed waiter Onaji Noa from 1997 to 1998, former back-up dancer Cris Judd from 2001 and 2003 and Marc from 2004 to 2014. Alex was married to Cynthia from 2002 to 2008.