The Canadian light-heavyweight needed surgery after he was knocked out by Ukrainian Oleksandr Gvozdyk this month.
Simone 'SiSi' God said the 41-year-old was recovering "in the private company of his family".
"Adonis is a world champion and is exhibiting that same determination in his recovery," she said.
"Despite recent reports being leaked to media, I wanted to clarify that Adonis is awake."
Stevenson, boxing's oldest and longest-reigning champion, was making his 10th WBC title defence when he was injured.