The seven-year-old's odds have halved into a general 4-1 and he is now favourite with some firms for the £130,000 contest.
Thunder Rock, who is rated 146, chased home subsequent Coral Gold Cup winner Datsalrightgino in the Grade 2 Future Champion Novices' Chase at Ayr in April before beating Mahler Mission, who was second at Newbury, on his seasonal reappearance at Carlisle last month.
Murphy, who landed Sandown's Listed novice hurdle with Booster Bob on Saturday, said: "The December Gold Cup is the plan and he’s been trained specifically for the race since he won at Carlisle.
"He’s been in very good form since then and I’m looking forward to running him. There’s plenty of form stacking up well for him, which is good to see, and he’s got the right sort of mark for the race.
"It’s going to be his first run in a big handicap and we'll have to see how he handles that experience, but I think he has a really attractive profile for the race, he’s in good form and it’s a good prize."
Thunder Rock beat Mahler Mission by three and a half lengths in the Listed Colin Parker Memorial Chase at Carlisle, when he was ridden by Sean Bowen, who secured his third Grade 1 success with Not So Sleepy in the Fighting Fifth on Saturday.
"It was a good performance at Carlisle last time and Sean got on well with him," said Murphy. "Getting that little bit more experience over fences before we tackle a big handicap like this was important.
"I actually thought he ran very well over course and distance last season in the Dipper. He handles the track fine and I don’t think there is going to be a massive field looking at the entries.
“We looked at the Peterborough Chase, which was sadly off, and if he was going to win a race like that then he must have a very good chance of winning a handicap off a mark of 146 for a lot of money.”
Betfair spokesman Barry Orr said: "We introduced him at 8-1. That was quickly taken, the same for 6-1 and we're now a defensive 4-1. The form of his three most recent runs have all been significantly franked so it's easy to see why punters have latched on to him."
Thunder Rock had a productive novice chase campaign last season, winning twice before running four times at Graded level, including when third behind Gerri Colombe in the Grade 1 Scilly Isles Novices' Chase.
"I threw him in at the deep end a few times last season and turning in at Sandown in the Scilly Isles I thought he would win," said Murphy. "He ran well when you look at what the winner has done since.
"He then went to Cheltenham and I didn't feel he stayed three miles in the Brown Advisory. Things didn't quite go to plan at Ayr and he might have been a slightly unlucky loser after missing the last.
"I hope he has a future in Graded chases, but Saturday will tell us an awful lot more. He jumped well at Carlisle and hopefully he will be big enough and robust enough to carry on as a chaser."
A total of 23 horses, including Il Ridoto and So Scottish, are in contention for the December Gold Cup, which was called off last season when the track at Cheltenham was frozen.
Virgin Bet December Gold Cup Handicap Chase (1.50 Cheltenham, Saturday)
Betfair Sportsbook: 7-2 Il Ridoto, 4 Thunder Rock, 6 So Scottish, 8 Fakir D'Oudairies, Fugitif, In Excelsis Deo, 9 Frero Banbou, 10 Complete Unknown, Richmond Lake, 12 bar.