Jennifer Lopez and Alex Rodriguez have started house-hunting together

A source said: "Jennifer and Alex are looking at apartments together that would be large enough for the both of them and their children.

Jennifer already has a beautiful place in NoMad, but Alex is currently based in Miami and doesn't have an apartment in the city."

Jennifer, 48, is poised to spend a lot of time in the coming months in the Big Apple, where she will be filming her new show 'Shades of Blue'.

And Alex - who played for the New York Yankees during his baseball career - sees relocating to the city as the most convenient way of spending more time with his girlfriend.

The insider told the New York Post newspaper's Page Six column:

"Jennifer will be in Manhattan a lot filming her NBC show 'Shades of Blue,' and Alex wants to be here with her. They are totally inseparable."

Rumours of their relationship hotting up come shortly after Jennifer - who has nine-year-old twins Max and Emme with her ex-husband Marc Anthony - spoke in glowing terms about the retired sports star.

She recently said: "I'm in a good relationship. I feel like I can say that for the first time - I don't know - maybe ever.

"And not that I didn't have great relationships, full of love and adventure, but this is the first relationship I've been where I feel like we really make each other better.

"We complement each other, and there's really pure, true love. Just wanting to support the other person and make them happy. So there's a different selflessness in the love that's beautiful and different. And healthy!"