As the Giants enter their bye week for the opening round of the playoffs, Gilbride is expected to take the opportunity to interview for the job. New York (12-4) is the NFC's top seed and has home-field advantage throughout the postseason.
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However, Raiders sources tell Mortensen that interim head coach Tom Cable has a solid chance of retaining the post.
Cable moved into the role when Raiders owner Al Davis fired Lane Kiffin four games into this season. Cable won two straight games to finish the season and was 4-8 as head coach.
Cable is expected to meet with Davis soon. The owner did not travel with the team to Tampa Bay for the regular-season finale because of a leg injury.
"I want to be the head coach of the Raiders, but it's not in my hands," Cable told reporters after Sunday's game. "But I certainly know I put this team together and got it going in the right direction, and [Sunday's win] proved that."
The Giants promoted Gilbride from quarterbacks coach to offensive coordinator after the 2006 season. The former offensive coordinator with the Houston Oilers, Jacksonville, Pittsburgh and Buffalo was a head coach for the San Diego Chargers.