Rico remained in serious condition in an intensive unit, but doctors said the injury was progressing favorably and that hey have stopped sedating him.
The 29-year-old Spanish goalkeeper, who previously played for Sevilla and is a reserve at PSG, got injured in Seville when he was headed to a mass with his relatives and was struck by a horse.
Rico had been in a medically-induced coma for 10 days following a riding accident, the hospital in the Spanish city of Sevilla treating the player said on Wednesday.
The Spaniard suffered severe injuries after being hit by a mule cart and a horse while taking part in an annual pilgrimage in southern Spain on May 28, his family said.
Rico had been given permission by PSG to take part in the pilgrimage, according to his family.
The hospital said it would issue a new statement on Friday unless there were significant changes before then.
Information from Reuters and The Associated Press was used in this story.