The Black Cats are currently languishing in last place on the Championship standings and have been without a manager since they parted ways with Simon Grayson.
Yorke is keen to get into management but what could work against him is his lack of experience.
He has yet to manage a notable club and his only notable experience came when he was assistant manager of the Trinadad and Tobago national team.
When asked if he is interested in the Black Cats job, Yorke said: "I have tried to get hold of [chief executive] Martin Bain and left a message or two to see if there is any comeback.
"The place needs a lift, something new, something exciting.
"They have gone for experience in the past. They have tried that and it hasn't quite worked out. Why not give it to someone new who is really eager to prove he can do the job?
"An interview would be nice. I will still continue to work at that and see where I get."