According to The Sun, Rihanna has continuously been texting him since they met on the set of The Graham Norton Show before Christmas.
A clip of the chat show featured Farrell paying a compliment to Rihanna's slender limbs. He said: "They are very nice limbs. There's probably a reason I mentioned them, I had to get them off my mind."
The conversation then turned to Rihanna discussing a wax treatment that had Farrell looking very excited.
A source close to Farrell claimed that the infamous Colin, who is known for being charming, was taken aback by some of Rihanna's flirty SMS texts, but he said that there was no harm since they are both single.
Colin Farrell's previous relationship with Alicja Bachleda-Curus ended last month. The two have a 16-month-old son, Henry.
The R&B chart-topper and Irish playboy have plans to meet when their schedules allow. The two have made headlines for other reasons too.
Farrell had starred in a leaked sex video tape and Rihanna's latest music video, "Te Amo", was controversial for the scenes that showed two women kissing each other.
Rihanna responds to 'S&M' controversy
Rihanna has responded to controversy surrounding her new single 'S&M'.
The singer, whose latest track includes lyrics about "whips and chains" and accompanying video includes a number of provocative outfits, admitted that the song's success is down to it's contentious nature.
"I don't think people would have been that curious if there wasn't some controversy involved," she told Extra.
"'S&M' is my favourite video I've ever done, and I can't wait to keep making more incredible videos and beating them out every time. 'S&M' is going to be a hard one to beat."
Discussing her upcoming world tour with Cee Lo Green, she confessed: "I'm really excited about [it]. We're just starting to put it together, and it's going to be even bigger than my last tour which I didn't think [was possible]. The 'Loud' tour is going to be special.
"He's someone I'd go and see in concert, so having him on tour with me was amazing." The star also revealed that a second, secret "special guest" will join her on the jaunt.