The seven-year-old completed a hat-trick of victories last season before finishing a fine sixth in the Cheltenham Gold Cup.
Second to A Plus Tard in last month's Haydock Grade 1, hopes were high that the lightly-raced gelding, owned by Susannah Ricci, would be poised to run in Kempton's Boxing Day feature. However, he remains on the easy list.
Williams said: "He won't be running in the King George. I can't say for sure how long he will be sidelined for.
"He got a wound at Haydock which had to be stitched and it has taken a while to get better.
The in-form Kings Caple-based trainer is also mulling over options for Commodore, who jumped his eight rivals into submission at Cheltenham on Saturday.
The Agetur Classic Chase at Warwick is widely regarded as a trial for the Grand National, which Williams won in 2009 with 100-1 shot Mon Mome.
Yet after seeing Commodore record a 15-length success under Charlie Deutsch in fine style at Cheltenham, she remained coy about the possibility of sending the nine-year-old to Warwick on January 22 for the three-mile-five-furlong Grade Three event.
Williams said: "I'm not saying Warwick is a plan. I haven't really had a chance to discuss it with the owners yet whether the Classic Chase is a possibility, so I'm not going to say that is the plan."
One For Arthur landed the Classic Chase en route to victory at Aintree in 2017, and asked whether the Grand National could be a long-term target for Commodore, Williams teased: "You are ahead of the game with that!"