The 85-year-old Attenborough, who directed "Ghandi" and acted in "Jurassic Park," had fallen into a coma after the Dec. 18 accident but has since regained consciousness.
Attenborough remains at St. George's Hospital, The Daily Telegraph reported Saturday.
The British newspaper said the Oscar-winner has suffered from an irregular heartbeat that led to a sudden blackout last summer.
Notable deaths of 2014 [PHOTOS]
Teresa and Joe Giudice distant since sentencing