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.
The Raiders also strongly denied a report by ESPN's Chris Mortensen that Davis was in discussions to sell at least 10 percent of the team to C. Dean Metropoulos, a billionaire seeking to buy a team to move to Los Angeles.
The Raiders sold 20 percent minority interest in the team in 2007 to a small group of investors in a deal that gave the group no option to buy the team. ESPN, citing unidentified sources, reported that Metropoulos is trying to negotiate a purchase option within three to five years of closing the deal.
"Chris' report is not true," Raiders CEO Amy Trask said. "We are not negotiating with this group. We know who they are and that they want to purchase the controlling interest in a team. This team is not available to them. They are unhappy about that and have turned to Chris to assist them in their efforts, which is easy to do since Chris contacted no one with the Raiders to ascertain if there was any truth to his report. There is not. It would have been so easy for him to contact us and ask if we are negotiating with this group. We are not."
Mortensen said in an e-mail that he stands by his report.
"The Raiders have lost the privilege with me of running stories past them for comment," he said. "This stems from their history of denials to most stories I have reported — as well as others in the media — when those stories have eventually proven to be true. The latest example is I reported that Al Davis planned to interview Giants offensive coordinator Kevin Gilbride and, of course, the story was trashed by a team spokesman."