The eight-year-old really put the first-season trainer on the map when winning a valuable handicap at Ascot in December.
Murphy elected to sidestep the Betfair Hurdle at Newbury to keep his powder dry for Cheltenham, and the Warwickshire-based trainer is likely to send his stable star for a racecourse gallop later this week ahead of either the two-mile County Hurdle or the Coral Cup over five furlongs further.
"He seems in great form. He's going to gallop at the end of the week, maybe at Warwick after racing on Friday," said Murphy.
"I'm very happy with him, but I'm still a bit undecided about whether I'm going to go County or Coral Cup.
"We'll just wait and see what the weather does but he's bang on course for one of them and we're all really excited."
Hunters Call is a best priced 20-1 for the Coral Cup on the Wednesday of the showpiece meeting and 12-1 for the County Hurdle on the Friday.
Select any odd to add a bet