Deadline reports that Ron Howard is the front runner for the directing gig, while acknowledging that Lawrence Kasdan has been mentioned as a possible replacement. Another report from The Hollywood Reporter claims that Joe Johnston, who started his career by working on the visual effects for the original Star Wars trilogy, has also been mentioned as a possible replacement. That report also includes new details about how Lawrence Kasdan may not even be allowed to replace Phil Lord and Chris Miller.
There are already rules in place at the Director's Guild of America (DGA) that prevent anyone already working on a movie to take over for a director that is being replaced, with the only exception being for a "short-term emergency." Since Lawrence Kasdan co-wrote the Han Solo spin-off script with his son Jon Kasdan, these rules may prevent the filmmaker from stepping in as a director. Lawrence Kasdan had also revealed in 2015 that Han Solo: A Star Wars Story will be his last Star Wars movie, after writing or co-writing the screenplays for The Empire Strikes Back, Return of the Jedi and Star Wars: The Force Awakens, and he has also directed hits like Body Heat, The Big Chill and Silverado.
Whether it's Ron Howard, Joe Johnston or another filmmaker, whoever replaces Phil Lord and Chris Miller may not even get credit for his or her work. Given that they were fired with just a few weeks of the shoot left, LucasFilm would most likely prefer that the new filmmaker get director's credit, but since Phil Lord and Chris Miller were on set filming since February, which obviously gives them strong grounds for directorial credit, although the new director will oversee the post-production process and the reshoots which have already been scheduled for this summer. However, it's entirely up to the DGA, as to who gets directorial credit, and unlike the Writers Guild of America, there is no appeals process, meaning the DGA's decision is finale. It's also unlikely that the guild will give credit to Lord, Miller and their successor, since the DGA is already not terribly fond of two directors on one movie. The guild's rules state that there shall be only one director for film, but waivers can be granted, which have become more and more commonplace in recent years, especially for more established directorial teams.
Another report from The Hollywood Reporter speculates that Han Solo: A Star Wars Story may even become an "Alan Smithee" film, although that won't happen since that pseudonym has been discontinued since 2000. For decades, if a filmmaker was so unhappy with the final cut of the film that he wanted his name taken off, the name that was put on the film instead was "Alan Smithee." The name was discontinued in 2000 after the film Burn Hollywood Burn used Alan Smithee as an actual character, played by Eric Idle, and after the real meaning of the name became more well-known throughout Hollywood.
This report also states that, whoever takes over the project, will spend the next several weeks, with production shut down, to go over the footage that has already been shot, re-edit the material that has already been filmed and pick up production from there. Despite this unique setback, Han Solo: A Star Wars Story will not be moved from its May 25, 2018 release date, but that could change if it takes longer than planned to find a director. Still, with three solid candidates in play, we may hear who's directing this Star Wars movie sooner rather than later.