According to RIA Novosti, the condition of the 45-year-old Russian does not change and remains stably heavy.
On January 10, the skater was hospitalized and placed in the intensive care unit.
Later, information appeared that he was connected to a ventilator.
Kostomarov is the 2006 Olympic champion, two-time world champion, three-time European champion, three-time Grand Prix final winner and three-time Russian champion.
At various times, Kostomarov's partners were Tatyana Navka, Ekaterina Davydova and Anna Semenovich.
Earlier it was reported that Kostomarov had left-sided pneumonia in combination with influenza B.