The 'We Found Love' singer, who was recently spotted leaving Kutcher's house, apparently believes the Two and a Half Men actor is "funny and cute".
A source told The Sun: "The flirting began as soon as Rihanna and Ashton met and swapped numbers.
"That moved on to texts and arranging to meet. They snuck off to a Santa Monica hotel a few weeks ago.
"They are two single people having a fling, so thought it would be best to meet in secret," the insider continued.
Rihanna has also supposedly been asking Kutcher about his belief in Kabbalah, a Jewish religious teaching.
"Rihanna has told friends he's funny and cute. Both of them love a good time and think they're too busy for anything serious just yet," the informant added. "She's starting to enquire about Kabbalah sessions with his rabbi."
Referring to Kutcher's ex-wife Demi Moore, the source added: "Ashton does not want to rub a new relationship in her face. She's still vulnerable. He's a good guy and, with all Demi's recent health problems, people have forgotten that."
Moore collapsed in January and was rushed to hospital with exhaustion as well as anorexia. She later entered rehab.
> Demi Moore meltdown 'not just about Ashton Kutcher'
Watch the video for 'We Found Love' by Rihanna below: