Adonis Stevenson's condition is improving "towards stable", according to the boxer's promoter Yvon Michel.
Stevenson lost his WBC light-heavyweight belt on Saturday night after being knocked out in the 11th round by Oleksandr Gvozdyk.
The Canadian was carried from the ring on a stretcher and taken to hospital, where his condition was initially described as critical.
Join DAZN and watch Canelo Alvarez vs. Rocky Fielding on Dec. 15
But Michel posted on Twitter on Sunday to say the 41-year-old had recently improved.
"Update on Adonis @AdonisSuperman: The state of Adonis has gone from critical towards stable from yesterday to today which is relatively good news. He is in controlled sedation to facilitate his recuperation," Michel wrote. "His family, his wife Simone and Groupe Yvon Michel would like to thank the many people who have taken the time to send comforting messages. New information will be published as we get it. No other comments will be made until then."