The 49-year-old continued to defy his years with a split-decision win over the Kazakh in Washington, as he added the WBA strap to his IBF championship.
Stevenson is the other big name in the division, but Hopkins feels that he can still hang with the best despite his half-century being on the horizon.
Before he reaches that milestone, the American wants to take on Stevenson and be crowned the undisputed light heavyweight champion to establish himself as still one of the best fighters on the planet.
"I want to be undisputed light-heavyweight champion this year," Hopkins told reporters. "The best fighter pound-for-pound is Floyd Mayweather and behind him is Andre Ward, but I ain't too far from the top three. I feel my age and the way I'm doing it, I'm not fighting cream puffs and I'm not done yet.
"I must be the undisputed light-heavyweight champion before I leave. We are with Showtime until I end my career and whatever fight it is I want to be light heavyweight champion before 50. Stevenson, I'm coming to Canada. I'm getting my papers together."
Stevenson, lineal, WBC and The Ring light heavyweight champion, has a title defence against Andrzej Fonfara on May 24.