Mouse Morris, His Song's Tipperary-based trainer, indicated he was keen to get in some match practice around Cheltenham with the novice before a return trip to Prestbury Park next March.
After watching His Song takeover from the front-running Greenflag Princess after two out - their closest pursuer, Space Trucker, slipped and fell on landing - to come home 11 lengths clear of Ollimar, Morris revealed his immediate plans for the David Lloyd-owned horse: "He's very agile and was quite clever out there so I'm looking forward to the Murphy's meeting with him.
"It would be great to have a run around Cheltenham next time with the future in mind," added Morris, who intends saddling the horse for the two-mile November Novices' Chase on the Sunday.
It was the third time in a row McCoy has partnered His Song to victory, having also been in the saddle when the gelding scored a bloodless win earlier in the month on the horse's chasing debut at Tipperary. At Punchestown last April, McCoy rode His Song to a hurdles win over French Ballerina.
Punchestown announced that the principal race at their December meeting, a Grade One IRpounds 45,000 event, will be named the John Durkan Leukaemia Trust Memorial Chase.