Fukunaga stepped down from the helm of the show following the completion of the first season of the anthology series, which starred Matthew MCConaughey and Woody Harrelson as troubled police detectives, and now Friedkin reveals he has met with True Detective creator Nic Pizzolato to discuss his possible involvement in the upcoming second season.
He tells IndieWire.com, "I am considering it (directing True Detective). I like this writer very much. I've met him, and he's the real deal as far as I'm concerned.
"Now, all the new seasons are different so I'm not committed - this new season has nothing to do with the last one. Except for him (Pizzolato) and his sensibility, which I think is extraordinary.
"So what you can say is I'm a huge fan of his writing, I've met with him, I like him, I like the direction he's taking with this."
The news emerges as True Detective lands four nominations for the 2014 Primetime Emmy Awards. Both Harrelson and MCConaughey will compete for Outstanding Lead Actor in a Drama Series, while Fukunaga is up for Outstanding Director for a Drama Series and the show is shortlisted for Outstanding Drama Series.
Season two is expected to be set in California and feature a whole new cast with three lead roles instead of the previous two.
Casting details have yet to be revealed, although Zero Dark Thirty star Jessica Chastain previously had to deny rumours suggesting she was preparing to sign on as a lead.