The four-year-old flashed home in the Flying Five at the Curragh on Sunday to be beaten just half a length by Karl Burke’s Havana Grey.
Son Of Rest is one of only two Irish-trained horses guaranteed a run in the race – which offers nearly £125,000 to the winner – along with Adrian Keatley’s G Force.
“It’s more likely he’ll run than not, I’d say,” said Stack.
“He ran a great race at the Curragh, we were thrilled.
“I’m not sure about his best trip. When he runs over five he finishes really strongly, but he does tend to run his best races over five.
“He did finish fourth in the National Stakes to Churchill as a two-year-old, though, so I’m sure he stays.
“The more rain they get the better, he loves it soft.”
Mark Johnston’s three-year-old Cardsharp has been left at the top of the weights with Great St Wilfrid winner Gunmetal, Perfect Pasture and Kimberella others towards the top.
There are still almost 170 horses entered for the Gold, Silver and Bronze Cups.