The 127 Hours star, who recently hit the headlines after posting an online clip of him lip-synching to RiRi's single You Da One, claims the 24-year old approached him to be her love interest in the promo - but he was unavailable.
Speaking to our US Team about Rihanna, Franco explained: "She actually asked me to be in that video, the one with the relationship that gets crazy."
He added: "I couldn't do it. But, I guess, I hope that that means there's mutual love between us."
The role was later offered to British model Dudley O'Shaughnessy - who Rihanna was said to have hand picked to play her destructive boyfriend - with reports at the time suggesting they briefly became an item after shooting the video.
Watch MTV News on the hour every hour on MTV - Sky Channel 126 and Virgin Channel 134