The 'Only Girl (In the World)' singer – who is currently single following her split from baseball star Matt Kemp in December – has reportedly been bombarding the Irish actor with mobile phone messages after the pair met on British TV host Graham Norton's chat show shortly before Christmas.
An insider told The Sun newspaper: "Colin was taken aback by some of the texts. He thinks he might well be in there. They're both single, so why not?"
On the show, the 34-year-old star admitted that he couldn't take his mind off the Bajan beauty's skimpy dress, which left only her "limbs" on show.
He said: "They are very nice limbs. There's probably a reason I mentioned them, I had to get them off my mind."
Colin – who has a 16-month-old son Henry with actress Alicja Bachleda-Curus and seven-year-old James with model Kim Bordenave – is now reportedly planning to meet up with Rihanna, 23, in Los Angeles whenever their hectic schedules allow.
Rihanna recently admitted she was keen to move on from her ex-boyfriend Chris Brown – who was convicted of assaulting her in February 2009 – but finds it "annoying" that people won't stop asking her about the incident.
She tweeted: "People won't stop askin abt it! Its f**kin annoying! Nobody wants to relive that, but some ppl can't respect that!
"I get it, they wanna raise awareness to young girls! But it ends up just makin me look bitter, pitiful, spiteful and angry! (sic)".