Nicky Henderson's eight-year-old was a fine winner of the Lanzarote Hurdle at Kempton on Saturday, for which he has gone up 6lb in the handicap.
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Walters won the Coral Cup with Whisper in 2014 and is happy to try for a repeat success with William Henry.
He said: "He did really well in the Lanzarote and we were very happy with him.
"We'll probably keep him hurdling this season and go back chasing next year.
"I've not really had chance to speak to Nicky, but he will most probably go down the same road as Whisper at Cheltenham."
Davy Russell is Walters' retained rider in Britain, but William Henry was ridden by James Bowen in the Lanzarote Hurdle.
When asked who would take the mount at the Cheltenham Festival, Walters said: "We haven't gone down that road yet."
Walters added he has not yet had an opportunity to speak to Henderson about plans for Whisper, who finished a disappointing fifth in the King George at Kempton on Boxing Day.
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