"I've talked to a lot of NFL people," Webb said after the Golden Bears' pro day workouts. "And double-digit teams have told me I'm a first-round guy."
The 6-5, 230-pound Webb, who was a graduate transfer to Cal from Texas Tech, was initially projected to be taken in the middle rounds. Recent buzz, however, has suggested that Webb's stock is climbing.
"Every meeting [with an NFL team] I've had, they've said I'm one of the best quarterbacks on the board," Webb said.
ESPN draft analyst Mel Kiper currently projects North Carolina's Mitch Trubisky and Clemson's Deshaun Watson to be the only two quarterbacks taken in the first round at No. 12 and No. 13, respectively.
On Friday morning, Webb threw in rainy conditions at Cal's pro day. Many of his passes went to fellow NFL prospect Chad Hansen, who logged 92 catches for the Bears this past season.
Webb says he has "about 12-15 more" meetings scheduled with various NFL teams. He declined to discuss further details, but when asked by a local Bay Area reporter, he did indicate that San Francisco 49ers coach Kyle Shanahan has been in contact.
Webb said scouts were happy with his throwing performance Friday. He's also been working to promote his mental grasp of the game to NFL teams.
"I try to show off a bit," Webb said. "I try to show them that I know my stuff, about defenses and about fronts. I think my potential is through the roof."
Webb plans to watch the NFL draft from his home in the Dallas area, where he will invite teammates from Cal and Texas Tech.
"It'll be interesting to see all those guys interact," Webb said. "Two different schools, two different years."