The two spoke Saturday after Gilbride had expressed interest in the job through his agent, Raiders senior executive John Herrera said Sunday.
Gilbride is the first outside candidate to talk to Davis about the job. Interim coach Tom Cable is also a candidate after running the team for the final 12 games following the firing of Lane Kiffin in September.
Gilbride's only previous head coaching experience in the NFL came in 1997-98, when he went 6-16 for the San Diego Chargers. Gilbride is a longtime assistant in the NFL and helped the Giants win the Super Bowl last season, then earn the top seed in the NFC playoffs this season.
The Raiders cannot talk to Gilbride again until the Giants are eliminated from the playoffs.
Cable is a serious contender for the job after winning the final two games of the season, including a season-ending victory over Tampa Bay that knocked former Raiders coach Jon Gruden's team out of the playoffs. Cable had a 4-8 record after replacing Kiffin.
Cable is still under contract until Jan. 13, and has talked with Davis over the past week about the team.