In a Wednesday afternoon news conference at the team's training complex, Ravens general manager Ozzie Newsome said that NFL franchises have made inquiries about both Harris and director of college scouting Phil Savage.
If Harris departs, expect the Ravens to promote assistant director of pro personnel George Kokinis, who has worked for owner Art Modell since 1991.
The Jaguars are splitting personnel responsibilities between the head coach and a general manager after firing head coach Tom Coughlin, who held the dual roles for eight years.
"Yes, James Harris has spoken with Wayne Weaver," Edwards said. "No, we don't have any announcement planned any time soon. Ideally, we would like to fill both positions as soon as possible. Maybe even by next week.
"Definitely, before the Super Bowl."
Former Minnesota Vikings coach Dennis Green, who interviewed Tuesday in Dallas with Weaver and Vance in Dallas, had originally expressed an interest in wielding considerable power over personnel, but has softened on that stance in recent days, according to published reports.
Now, Green apparently wants to work in tandem with former Cleveland Browns and San Francisco 49ers executive Dwight Clark. The Jaguars interviewed Buffalo Bills assistant general manager Tom Modrak on Sunday.
Another prominent name often linked with the Jaguars is former New Orleans Saints general manager Randy Mueller.
Prior to being named to his current post with the Ravens in 1997, Harris was the New York Jets' assistant general manager from 1993 to 1996 after six seasons as a scout with the Tampa Bay Buccaneers. Harris, 55, played quarterback in the NFL for 12 seasons, including stints with the Bills, Los Angeles Rams and San Diego Chargers.
"We have one of the most attractive jobs for people here in the NFL," Weaver told reporters in Jacksonville when he announced Coughlin's firing. "I think we're going to be able to attract the best and the brightest minds out there. We're going to talk to those people to determine who can help us rebuild and get back to our winning ways."