“He is comfortably at home in the Karkloof, KwaZulu-Natal, South Africa, where he is supported by his wife, Ann, and immediate family members,” the organisation stated.
“The family are most grateful for the well wishes they have received but request privacy during this period.”
An update would be given when there was a change in his condition.
Player, 87, suffered a stroke on Thursday.
He is credited with saving the white rhino from extinction in KwaZulu-Natal in the 1950s.
Player is the older brother of renowned golfer Gary Player.