WRAl-TV, Raleigh, N.C., said it learned that Stacy Lloyd III, son of heiress Rachel Mellon; his sons, Stacy IV and Thomas; and Thomas Lloyd's wife, Ricki, were called to testify Friday.
Its proceedings are secret, but the grand jury is believed to be probing the former Democratic presidential candidate's campaign finances on suspicion that funds were used improperly, including to hide Edwards' affair with staffer Rielle Hunter.
Hunter gave birth to a girl in February 2008 who Edwards has admitted is his daughter.
Mellon, 100, has been interviewed by the FBI at her estate in Upperville, Va. She gave $3.4 million in 2007 to a non-profit backing Edwards' candidacy.
She also gave $700,000 to Andrew Young, a former Edwards aide who pretended to be the father of Hunter's child during the 2008 campaign. The money is said to have gone to Hunter's expenses.
Sources told WRAL the Lloyds have no knowledge about the money Mellon gave Edwards but were expected to testify about how she might have been drawn into a cover-up of the affair.