According to Tim Kawakami of the San Jose Mercury News, Gruden has had a "flirtation" with Raiders owner Mark Davis for more than a year.
Rapoport also said Gruden told the Raiders to select quarterback Johnny Manziel in the first round of this year's NFL draft.
Gruden has been employed as an analyst for ESPN on Monday Night Football since 2009, several months after being fired from being the head coach of the Tampa Bay Buccaneers. Before joining Tampa Bay, he served as the Raiders' head coach from 1998-2001, helping the team make the playoffs his last two years for the first time since 1993.
Davis's father, Al, was the team's owner during Gruden's previous Raiders stint. Al engineered the trade that sent Gruden to the Buccaneers in 2002.
Gruden's name has often come up when head coaching jobs have opened the past several years but he hasn't come close to accepting any positions. He's never given a firm indication publicly that he's interested in returning to coaching.
The Raiders are currently being coached on an interim basis by former Miami Dolphins head coach Tony Sparano. Dennis Allen was fired as head coach after the team's 38-14 loss to the Miami Dolphins in Week 4. Allen went 8-28 with the Raiders.
Gruden amassed a 100-85 overall record, including the playoffs, in 11 seasons as the coach for the Raiders and Buccaneers.
Oakland has had seven head coaches since Gruden was traded, including five (counting Sparano) since 2007.
The Raiders are 0-6 this season and are the last winless team in the NFL. They play the Cleveland Browns on Sunday.
- Ben Estes