He's was introduced as a major villain in the second movie, so how would Dane DeHaan's Green Goblin have figured into The Amazing Spider-Man 3? After spending years trapped in development hell with directors such as Tobe Hooper and James Cameron (Aliens) attached at different stages, Spider-Man finally hit the big screen in 2002. It proved to be worth the long wait, with Sam Raimi's movie being packed with both heart and action. Raimi would top his work with Spider-Man 2, which is arguably one of the best comic book movies ever, though Spider-Man 3 would famously prove to be a letdown.
The movie was overstuffed with subplots, characters, and villains, with the producers insisting Raimi use Venom, despite the director's lack of interest in the villain. While the sequel was another success it left a bad taste with audiences, so Raimi intended to make a fourth entry that would win them over again. Unfortunately, the director was unhappy with how the screenplay for Spider-Man 4 was progressing and decided to step aside. This led to the character being rebooted with The Amazing Spider-Man series. While Andrew Garfield's work as Peter Parker was well-received, reception to both movies was mixed. The second movie, in particular, repeated a lot of the problems that befell Raimi's third movie; chiefly, too many villains and subplots.
The Amazing Spider-Man 2 is considered one of the webslinger's weakest, and plans for a third entry and a Sinister Six movie were quickly cancelled. The second movie set up a lot of cliffhangers for future movies, with Peter's former friend turned enemy Harry Osborn (Dane DeHaan) set to feature prominently. Harry transformed into villain Green Goblin in the finale of The Amazing Spider-Man 2, causing the death of Gwen Stacy and ending the movie committed to Ravencroft Institute.
It certainly feels like DeHaan's Green Goblin was shaping up to be the main villain of the next movie, though it appears Sony's plans were a little more complex. The second movie also introduced Norman Osborn, who was played by Chris Cooper (Cars 3). Norman only appears in a couple of scenes before dying, though the movie originally ended with a teaser revealing his head had been cryogenically frozen. In fact, it appears a number of deceased characters were supposed to return for The Amazing Spider-Man 3, including Gwen Stacy and her father George, with Peter himself inventing some kind of formula to bring back the dead.
With both a Sinister Six movie and a third Spider-Man, that leaves the question of how exactly Dane DeHaan's Green Goblin would have fit. Chris Cooper once stated he was guaranteed to return for a third movie, though director Marc Webb (500 Days Of Summer) would later reveal Norman's Green Goblin was set to lead the Sinister Six movie instead, which was going to come before The Amazing Spider-Man 3. Interestingly, Harry Osborn isn't ever called Green Goblin in the second movie or the video game - though he's credited that way - meaning that name might have been reserved for Norman's eventual reappearance, with Harry becoming the Hobgoblin instead.
It appears plans for either movie were never completely locked, however, with some reports stating Spider-Man himself would have been a featured character in Sinister Six, whilst others state he would only have made a cameo. Given the personal relationship between Peter and Harry, it's likely the Dane DeHaan Green Goblin would have been the main threat of the third movie. The second movie saw Harry put steps in motion for The Gentleman to assemble the Sinister Six to assassinate Spider-Man. After that (presumably) failed, The Amazing Spider-Man 3 likely would have seen Harry released or escape from Ravencroft to take his revenge on Peter.