The Grade One contest - set to feature Gordon Elliott's exciting prospect Samcro - is one of two potential options for the six-year-old, along with the Albert Bartlett Prestige Novices' Hurdle at Haydock later in the month.
Mulcahys Hill was narrowly denied a hat-trick when a narrow runner-up in last month's Challow Hurdle at Newbury.
Greatrex said: "We've sort of discussed it and we thought we would put him in the Irish race. It shows that we are quite dynamic.
"If it looks very hot we probably won't go over there as we have options over here. We will sit down and look what is in the race then take a view.
"If there were five or six good ones in there we would then sit tight and wait for the Haydock race.
"He has definitely improved since Newbury and he seems in good form at home."
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