The Grade Two prize is one of two races the Barbury Castle Stables handler is weighing up for the six-year-old, along with the Betfair Hurdle at Newbury seven days earlier.
After landing the Greatwood Hurdle at Cheltenham on his penultimate start, the Elite Racing Club-owned gelding finished sixth in a valuable handicap last time out at Ascot.
Elgin is currently a best-priced 20-1 for the Betfair Hurdle.
King said: "He is going to be top weight in the Betfair Hurdle, so we might have a look at the Kingwell. He is in very good form and is fresh and well.
"It would be an almighty difficult ask to win a Betfair off top weight, as I know a few at near the top are not going to run, so the Kingwell is a consideration.
"He ran very well at Ascot, but they didn't go that hard up front and he is better off a real strong gallop."