As part of Webb's initial deal with Fox, he signed on to direct at least two films for the studio. When he got the job on the Spider-Man reboot, however, Fox allowed him time to run off and make that movie, but now it's been three years since his feature debut, and Fox would understandably like to exercise Webb's obligation now that he's made a successful 3D blockbuster.
Neither Sony Pictures not Fox are publicly commenting on it at this point, but 24 Frames is reporting that Fox is potentially in a giving mood. Apparently, the studio is considering letting Webb hand over another rain check on his obligation. Not for free, of course. The ability to make the Amazing Spider-Man sequel would come on the condition that Webb sign a two-movie deal with Fox. Webb is reluctant to do so, since he's in very much in-demand right now and not eager to find himself in a similar quandary. Still, he also wants to continue the adventures of Marvel's beloved webslinger.
Whatever happens should happen pretty soon here. Sony announced a May 2, 2014 release date for the as-yet untitled sequel almost a year ago, and with less than two years to go, time is of the essence. If Webb is out, Sony's going to need to find a new director in a hurry.
Roberto Orci and Alex Kurtzman are currently writing the screenplay, working from previous drafts by initial The Amazing Spider-Man writer James Vanderbilt. The duo will also produce the sequel, which again stars Andrew Garfield and Emma Stone as the rebooted Peter Parker and Gwen Stacy.