The Canadian star, 41, was placed into an induced coma after his shock defeat to Oleksandr Gvozdyk at the beginning of the month.
Reports as soon as yesterday revealed there was little progress and that he still needed assistance breathing.
But in a media statement, Simone said: "We are so grateful for the outpour of messages, gifts and support that have come our way.
"Despite recent reports being leaked to media, I wanted to clarify that Adonis is awake.
"He is healing from his injury in the private company of his family and his dedicated medical team.
"Adonis is a world champion in the ring and is exhibiting that same grit, strength and determination in his recovery.
"Adonis and our family are so thankful to you all for your love and support and respectfully ask to continue to grant Adonis and our family privacy as he heals from this accident.
"With the holidays here, Adonis is spending time enjoying music and spending time with Adonia and his family and sends his love and appreciation to you all."
Stevenson was rushed to hospital after being knocked out in the 11th round at the Videotron Centre in Quebec.
He lost the WBC and lineal light-heavyweight titles but there were far deeper concerns as he was placed in an induced coma.
But thankfully he is making good progress and is making the early steps on the road to recovery.
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