The reality TV star - who recently split from American footballer Reggie Bush - was reportedly seen in a "very affectionate" embrace with the Real Madrid in the middle of a Miami restaurant, before following him back to his mansion.
A source told The Sun newspaper: "She and Ronaldo were kissing and very affectionate. They looked to be getting on really well, laughing the whole time."
The American socialite - who was holidaying in Miami when she met the hunky sportsman - allegedly went back to his place after the meal, staying for around four hours, before leaving in a chauffeur-driven Mercedes G-Wagon.
Kim, 29, had recently been linked with English soccer player Wayne Bridge, who she had been communicating regularly with by text message.
A source said: "They met while Wayne was cheering himself up on a boys' night out and got on like a house on fire."
This is not the first time Ronaldo, 25, has been linked to a famous American girl.
He was seen kissing hotel heiress Paris Hilton in a Los Angeles nightclub last July.
A source at the time said: "Cristiano and Paris were all over each other swapping spit the entire night! His table needed every waitress in the building to service the large quantities of alcohol, and he spent in excess of $20,000 on champagne and drinks."