They want it to be recorded testimony taken at her estate in Virginia.
And there's an unusual twist -- prosecutors have indicated that attorneys for Edwards would also be present for the questioning, but Mellon has not yet agreed to it.
A federal grand jury in Raleigh has been investigating Edwards for more than a year and a half.
According to sources, prosecutors are focused on the possible misuse of campaign contributions.
They want to know about the arrangement to conceal the affair and the baby John Edwards had with his mistress, Rielle Hunter.
Sources say prosecutors are gathering information about the people who donated money to help Edwards' former aide Andrew Young, his wife, and Hunter live a life on the run.
Young has said that some of the money came from Bunny Mellon, the wealthy widow of banking heir Paul Mellon.
Four of Bunny Mellon's relatives testified before the Raleigh grand jury in early December.
A source close to the case tells the I-Team, FBI agents have interviewed Bunny Melon in the past, but now if she agrees to the recorded testimony. Attorneys for Edwards could cross-examine her and that testimony could be used if he's indicted and the case goes to trial.
Prosecutors may be taking the unusual step because of Mellon's advanced age. Her information could become critical if the case goes to trial.