The Wilmcote handler has earmarked the extended two-mile-three-furlong Listed contest on February 7 as a potential target for the six-year-old.
The form of the Diana Whateley-owned gelding was given a significant boost on Saturday when Elixir De Nutz, whom he defeated on his hurdles debut at Cheltenham, claimed Grade One honours in the Tolworth at Sandown.
Murphy said: “We might look at running Thomas Darby in the Sidney Banks. I won’t be running him, though, when it gets really soft. He will have one more run, then go for the Supreme.
“A good gallop over two miles is what he wants, but he should be fine over the trip in the Sidney Banks as long as he settles.
“We were giving the winner weight at Kempton (Mister Fisher) – and it was on ground he didn’t like, and he was a bit keen.
“It was a good run – and the handicapper thought so, because he has put him up another 2lb. We’ve not seen the best of him yet.”
He said: “We might go to trials day at Musselburgh with Itchy Feet, then go to the Supreme. He is rated 142, and I think everyone has forgotten about him.
“He has won a Listed race and was second in a Grade Two, giving Colin Tizzard’s horse (Elixir De Nutz) weight.
“We have given him a winter break, and we will have him ready for the spring.”