Having previously finished second to Summerville Boy in the Tolworth Hurdle at Sandown, Kalashnikov is a best-priced 11-2 for the Supreme and pleased Murphy as he had a spin over hurdles in Newmarket on Thursday morning.
She said: "It all went very well. He's in good order so fingers crossed we can keep him that way until Tuesday.
"We're not too worried about the ground. It was soft at Newbury last time and he went through it and it was heavy at Sandown the time before, so he is pretty versatile.
"He's such a good-actioned horse that I'm sure better ground will suit him and he's also by Kalanisi, whose progeny tend to go well on quicker ground.
"I think we're all guessing a bit at the Cheltenham going. It's a quick-draining track so we will see what happens."
Kalashnikov was also entered for the two-mile-five-furlong Ballymore Novices' Hurdle, but Murphy said: "If he doesn't go there on Tuesday for any reason, he won't be running."
Murphy only took out her licence in September 2016 and with Mercian Prince also due to travel to Prestbury Park for next Thursday's Brown Advisory & Merriebelle Stable Plate, the Newmarket handler can hardly conceive her good fortune.
She added: "It's unbelievable and very exciting. It's very surreal to be going to the Festival with two live hopes and for a yard of our size, it's just fantastic."
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