The Llancarfan handler is contemplating making the Grade One contest at Newcastle on December 2 the next port of call for the six-year-old after he failed to feature on his return to the Flat in the Cesarewitch at Newmarket on Saturday.
John Constable has won his last two starts over jumps in the Swinton Hurdle at Haydock and the Summer Hurdle at Market Rasen.
Williams said: "He is back safe and sound and Jim (Crowley) said he was not 100 per cent happy with the horse, so he looked after him. The ground was very fast for him.
"I don't think John Constable or Evan Williams will be on the Flat again, we will stick to what we know!
"The Elite Hurdle at Wincanton will probably come too quick and I would probably say that I half tempted to put him in the Fighting Fifth as that is usually a single-figure field.
"We won't rush him back as he needs to have a couple of weeks just to forget about Newmarket."