Trainer Willie Mullins says Min is likely to run in the upcoming John Durkan Memorial Chase at Punchestown.
The eight-year-old won last year's renewal ahead of easing to a 20-length success in the J-L-T Chase at Aintree.
"Min could start off in the John Durkan," Mullins said of a potential run in the race next month.
"We were delighted with his performance at Aintree last season over two and a half miles and we’re looking forward to getting him started again. We have other entries but will decide closer to the time."
Cheltenham Gold Cup winner Al Boum Photo has also been entered while Grade 1 winners Delta Work and Shattered Love are possible runners for Gordon Elliott.
"We've got plenty of options for the John Durkan and we will just see how things go over the next few weeks but hopefully we will be well represented," Elliott confirmed today.
"Shattered Love had a lovely confidence booster in a mares chase at Clonmel last Thursday and that should have done her the world of good. She ran very well in the Durkan last year and hopefully we can get her back there in the same form this year."
Two-time Cheltenham Festival winner Presenting Percy is another likely runner.
"It's so far so good with him and the plan is to head to the John Durkan Chase, all being well,” said owner Philip Reynolds.
“He still has an important few weeks ahead of him and the next week or so will be crucial. All being well he will start off at Punchestown but we'll keep our fingers crossed between now and then."