A trilogy centring on Andrew Garfield's incarnation of Peter Parker/Spider-Man was confirmed earlier this month.
Columbia Pictures President Doug Belgrad spoke to The Hollywood Reporter about the future of the franchise, insisting that he'd love to see Webb return for the sequels.
"We'd really like him back, but there are obstacles," Belgrad said. "He has an obligation to Fox."
Webb is currently contracted to do another film with Fox following his first picture (500) Days of Summer, which starred Joseph Gordon-Levitt and Zooey Deschanel.
Emma Stone, who plays Gwen Stacy in The Amazing Spider-Man, credited the director with bringing "humanity" to the movie.
Watch Digital Spy talk to the cast of The Amazing Spider-Man below: