Richardson died Wednesday in a New York hospital at the age of 45. She had suffered a fatal brain injury during a skiing accident in Canada Monday.
The Telegraph said Redgrave, 72, stroked Richardson's face and sang to her film and stage star daughter as her life ebbed away.
The Daily Mail said Redgrave had sung the same song at her daughter's first wedding to producer Robert Fox in 1990.
Richardson had been married to her second husband, actor Liam Neeson, for 14 years when she died.
The New York Daily News said a casket containing Richardson's body was brought via hearse from the Greenwich Village Funeral Home to the Irish Historical Society Friday where a wake was to be held.
Some reports said Richardson will be buried upstate in Millbrook, N.Y., near where she and Neeson had a second home.