Garrett replaced Phillips in November after the team stumbled to a 1-7 start and has since guided the Cowboys to a 4-3 mark.
The Star-Telegram said the only thing preventing Jones from making it official is the NFL's "Rooney Rule," which requires that minority candidates be interviewed for any head coaching vacancy.
John Wooten, the chairman of the Fritz Pollard Alliance, told the newspaper Jones will interview current Cowboys receivers coach Ray Sherman as the "Rooney Rule" candidate.
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