According to reports in the US, the singer has been getting to know Maksim, who is a pro dancer on Dancing With The Stars, the US version of Strictly Come Dancing.
A source told People the pair are "friends and have been talking" but they are taking it slow and wouldn't classify themselves as a couple. Yet.
It's thought J.Lo was first introduced to Maksim via her best friend Leah Remini, who appeared on a past series of DWTS.
Jennifer also performed with Maksim at the 2013 American Music Awards last year.
A source told E! News: "Leah and Jennifer are best friends, so as a group, they're all very friendly. [Maks is] in India and [J.Lo's] at the World Cup right now. Who knows what could happen down the road?"
Jennifer's link to Maksim comes shortly after she split from boyfriend of two-and-half years Casper. Sources have said the break-up was "amicable" and the couple are still friends. Busy work careers and time spent in different cities was apparently a large factor.
Despite ending a long-term romance, the star appears to be keeping positive.
On 10 June, she tweeted a photo of herself beaming for the camera, telling fans: "Smile... #lifeisgood #samegirl #jloaka #7daystogo #JLoJune17 #brazil #hereicome #MundialBrasil2014."
She will perform at tonight's World Cup Opening Ceremony in Brazil.
Jennifer Lopez (@JLo) June 11, 2014
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