Jennifer Lopez and Alex Rodriguez Announce They Are Staying Together: 'We Are Working Through Some Things'

"They never officially broke up and talked about it but are still together," a source tells PEOPLE

Jennifer Lopez and Alex Rodriguez have announced they are staying together.

"We are working through some things," they said in a joint statement obtained by PEOPLE.

"They never officially broke up and talked about it but are still together. They hit a rough patch. But were not broken up," a source close to the pair tells PEOPLE. The source added that the speculation that arose last month that Rodriguez had had an affair after Southern Charm's Madison LeCroy "had no bearing on the rough patch at all. "

"She's working in the Dominican Republic and he's in Miami so it's tough seeing each other especially with quarantining and COVID," the source adds of Lopez and Rodriguez, "but they want to try to stay together."

A separate insider says, "This was not caused by a third party. Madison [LeCroy] or anyone else. They are working through things."

For more on where Jennifer Lopez and Alex Rodriguez stand, listen below to the episode of PEOPLE Every Day.

The announcement came hours after multiple sources confirmed to PEOPLE that Lopez, 51, and Rodriguez, 45, had split.

Rodriguez shared a post on social media earlier in the day Friday, posting a selfie atop a boat in Miami.

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

J-Rod got engaged in the Bahamas in March 2019 after dating for two years. Over the past year, the couple has spent time at home during the pandemic with their blended families — Lopez's 13-year-old twins Maximilian "Max" David and Emme Maribel with Marc Anthony and the former MLB player's daughters Ella, 12, and Natasha, 16, with ex-wife Cynthia Scurtis,

Earlier this year, Lopez talked about having to postpone their wedding two times because of COVID.

"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," the "In the Morning" singer told Elle. "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."

RELATED VIDEO: Jennifer Lopez Talks 'Prioritizing' Her Family's Health: 'It Became the No. 1 Thing We Took for Granted'

She also shared last month that the two had gone to therapy together.

"I miss being creative and running on 150," Lopez told Allure. "But Alex, of all people, was like, 'I love it. I love being at home. I love doing my Zooms. I love knowing the kids are there, and you're there all the time.' It has been actually really good."

"We got to work on ourselves. We did therapy," she explained. "I think it was really helpful for us in our relationship."

Last month, speculation arose that Rodriguez had had an affair after Southern Charm's LeCroy was accused of sleeping with a married MLB player. However, a source told PEOPLE then that the two had "never met."

Want to get the biggest stories from PEOPLE every weekday? Subscribe to our new podcast, PEOPLE Every Day, to get the essential celebrity, entertainment and human interest news stories Monday through Friday.