They said a memorial service for the actor and director, who died on Sunday aged 90, was being planned for later this year.
A spokeswoman for the family said: "Lord Attenborough's funeral will be a strictly private family funeral. The family have asked for no flowers but, if people wish, charitable donations can be made to Denville Hall."
He moved to the rest home for retired actors, in north-west London, in 2008 and his widow still lives there. News of his death sparked tributes from politicians, Hollywood stars and industry leaders.