Per Sports Illustrated's Ben Baskin, Webb is willing to wait for his opportunity to lead the Giants when Manning steps down.
"I know I'm going to get a shot here," Webb said. "If it's tomorrow, if it's in 10 years, I know I'm going to get a chance. And when that comes, throw it deep, throw it deep. Scared money don't make money."
Manning, who turned 37 in January, is coming off one of his most difficult years in the NFL. His 19 touchdown passes were the second fewest of his career over a full season, surpassing only his 2013 campaign in which he tallied 18 touchdowns and led the league with 27 interceptions.
Former Giants coach Ben McAdoo benched the four-time Pro Bowler in favor of Geno Smith for one game in Week 13 against the Oakland Raiders, ending the longest consecutive-starts streak by an active quarterback at 210.
The Giants selected Webb in the third round last year. The 23-year-old didn't appear in a game as a rookie but is expected to serve as Manning's backup in 2018.