Alex Rodriguez has flown to Los Angeles to spend time with Jennifer Lopez

Jennifer, 47 and 41-year-old Alex also worked out together at her trainer Gunnar Peterson's gym and have been spending quality time together at her Bel-Air home, according to E! News.

And it has been claimed that things are getting serious between the pair.

An insider recently said: "All his friends can tell he really likes J.Lo [but] in the beginning they thought this may just be a fling. Friends are slowly thinking this may actually be a great match. He calls J.Lo his 'lady'. He would wife her up in a heartbeat...she is different than other people he's dated."

The pair are believed to have met at one of the singer's shows in Las Vegas last month.

Meanwhile, Jennifer's former husband Marc Anthony, 48 - who was married to the 'Shades of Blue' actress for 10 years until 2014 - recently insisted she is his "girl for life".

He said: "If you want to get along with a woman, just get divorced ... I'm producing her Spanish album, which is, I'm telling you right now, some of the best work I've ever done and some of the best work that she's ever done.

"The fact that she put her career in my hands is a massive responsibility, but no one knows her like I do ... We've always been good friends from day one, you know. We met working, 20-something years ago ... She's my goombah. That's my girl for life."

And Jennifer - who shares nine-year-old twins Max and Emme with Marc - previously admitted the couple's split was "good for the whole family".

She said: "At first I was like, 'We're good with the kids and everything, but if we start working together, are we gonna start going at each other again?' And it's been awesome. Honestly, I think it's even helped our relationship.

"We're just in a really great place, and the kids get to spend time with the two of us more together and see us working together. It's just good for the whole family."