Road To Respect provided Meade with a first Cheltenham Festival winner over fences in March when scoring in handicap company, and he successfully stepped up to Grade One level at Fairyhouse at Easter.
He continued his progression on his return to action, winning the Irish Daily Star Chase at Punchestown.
Disko has always been held in the highest regard by Meade and after finishing third in the JLT at Cheltenham, he relished the step up to three miles at Punchestown, running out an easy winner of the Growise Champion Novice Chase.
There are two suitable races for both horses, the Grade One JNWine.com Champion Chase and the Grade Two MyCarNeedsA.com Chase over two and a half miles.
"At the minute it looks like both Disko and Road To Respect will run in Down Royal," said Meade.
"In which race, I'm not sure, but Michael (O'Leary, owner of Gigginstown House Stud) is quite keen that the two of them run.
"Both are well at the minute. Road To Respect came out of the race at Punchestown good, and Disko worked (on Wednesday) and was in great form."