The director previously looked unlikely to return to the Columbia Pictures franchise for a second film, due to a contractual commitment with Fox Searchlight.
Fox is considering allowing Webb to return for the Amazing Spider-Man sequel in return for upping his contract with the studio from one film to two, according to Los Angeles Times.
Webb and Columbia are both reported to be keen to see him helm the follow-up to the Emma Stone and Andrew Garfield-starring movie.
Screenwriting superstars Alex Kurtzman and Roberto Orci have been hired to work on the script for the comic book movie sequel.
Columbia/Sony declined to comment on the rumours and a Fox spokesperson was not immediately available.
Watch a trailer for The Amazing Spider-Man below: