The former Leeds, Newcastle and Real Madrid centre-back has had an injury-ravaged career, but has still represented his country on eight occasions.
As he moves into the latter stages of his playing days, the 33-year-old is considering his options once he does hang up his boots.
"I've done OK in my career, I could have done a lot better," he told the club's official website.
"Football is the only thing I know. Hopefully one day I would like to be a coach or a manager. I want to be a manager and to get inside players' minds.
"Every manager I have played for has left an impression, good and bad. I have learned from every one of them, but you go in as your own person and do it your own way."
Having already done his level two badges after gaining experience with Boro's academy, Woodgate feels he is the right place to continue his development.
"This is the perfect place to do a coaching badge, with Dave Parnaby and his Academy," Woodgate added
"You have to understand the players, what makes them tick. You have to treat each of them differently."