The 85-year-old composer has confirmed he wants to be involved in the forthcoming film, which comes shortly after the movie music legend revealed he is working on a theme for the Han Solo 'Star Wars' spin-off.
Speaking about 'Episode IX', he told Variety: ''I would very much like to complete that.''
Williams has amassed an incredible 50 Academy Award nominations to date - more than any other living person - and his latest work on 'Star Wars: The Last Jedi' and 'The Post' could see him top that number.
The composing star - who won Oscars for his scores for movies such as 1977's 'Star Wars', 'Jaws' and 'E.T.' - recently confirmed he is creating a theme for 'Solo: A Star Wars Story'.
Williams - who has created the score for all of the 'Star Wars' movies to date except one, 'Rogue One: A Star Wars Story' - said: ''The present plan is that I'm writing a theme for Han Solo, and John Powell is going to write the score, which he'll do brilliantly.
''His assignment is something I'm very happy about. What I will do is offer this to John, and to Ron Howard [director], and if all parties are happy with it, then I will be happy.''
'Solo: A Star Wars Story' will focus on the early years of Han Solo, the Millennium Falcon-owning space smuggler originally played by Harrison Ford.
Alden Ehrenreich is taking over the iconic role from Ford, who portrayed the character in four films and for the final time in 2015's 'Star Wars: The Force Awakens'.
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