Min is likely to spearhead Willie Mullins' quest for another win in next month's John Durkan Memorial Chase at Punchestown.
Successful in the race last season, Min went on to win further Grade Ones at Leopardstown and Aintree.
While Mullins also has Gold Cup winner Al Boum Photo, Douvan, Chacun Pour Soi and Un De Sceaux entered up on 8 December, he has nominated Min as the most likely of his runners.
"Min could start off in the John Durkan," said Mullins.
"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."
Another who could reappear in the race is Pat Kelly's Presenting Percy, who picked up an injury in the Gold Cup when he last ran.
Owner Philip Reynolds said: "It's so far so good with him - and the plan is to head to the John Durkan Chase, all being well.
"He still has an important few weeks ahead of him"
"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."
Gordon Elliott has five entries - including Delta Work - and his mare Shattered Love, who returned to winning ways recently, could aim to go one better than last year.
"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," said Elliott.
"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 I hope we can get her back there in the same form this year."
There is one entry from Britain among the 23, Ruth Jefferson's Waiting Patiently. The last non-Irish-trained winner was Paul Nicholls' Noland in 2008.