The '127 Hours' star had allegedly tried to get Lucy Clode, 17, to his hotel room after meeting her outside the Longacre Theatre, where he is performing in the play 'Of Mice and Men', reported Ace Showbiz.
A private conversation had apparently happened between Franco, 35, and the Scottish girl which got leaked online on Wednesday.
Franco responded to the rumours by posting a photo of himself with a message on twitter.
"Why are you thirsty for underage ones? I'm not! I hope parents keep their teens away from me! Thank you," he wrote.
It is speculated that this is nothing but a publicity stunt for Franco's new movie 'Palo Alto' in which he is playing the character of a high school teacher who happens to have an affair with one of his teenage students.