The Liverpool boxer taunted his opponent in the pre-fight press conference, suggesting that he was knocked out by a journeyman fighter, referring to Stevenson's defeat to Darnell Boone.
Bellew said: "It has been 12 weeks of long, hard work and I have been thinking about him morning, noon and night.
"All I want to do is nail him. Whatever it takes and whatever I've got to do I will and on Saturday night I am going to be world champion."
Saturday's bout will be Bellew's second world title shot, having lost to Nathan Cleverly in 2011.