Min is one of 13 contenders for Willie Mullins among a total of 44 entries for the Ryanair Chase at the Cheltenham Festival.
The eight-year-old has run at the showpiece meeting on two previous occasions, finishing second to Altior in both the 2016 Supreme Novices' Hurdle and in last season's Queen Mother Champion Chase.
He made a successful start to the current campaign in the John Durkan Memorial Punchestown Chase last month and is favourite with some bookmakers to make it third time lucky at Cheltenham in this two-mile-five-furlong Grade One.
Mullins has also entered Un De Sceaux - winner of the Ryanair two years ago and second last year - as well as Al Boum Photo, Footpad and Kemboy, among others.
There are a record 29 Irish-trained entries overall, with last year's winner Balko Des Flos - trained by Henry de Bromhead - and Gordon Elliott's JLT Novices' Chase heroine Shattered Love also in the mix for the raiding party.
The home team is headed by Waiting Patiently.
Ruth Jefferson's stable star won his first six starts over fences - including a top-level success in the Ascot Chase last February.
He made his first start since in the King George VI Chase at Kempton on Boxing Day, but unseated jockey Brian Hughes after being badly hampered by the fall of Bristol De Mai and connections are now considering their options ahead of a possible trip to Prestbury Park in March.
Waiting Patiently has not been entered in the Champion Chase or the Cheltenham Gold Cup, meaning the Ryanair is his only viable option.
Other hopefuls for Britain include the Paul Nicholls-trained pair of Frodon and Politologue and Venetia Williams' Aso, who was third behind Un De Sceaux in the 2017 Ryanair and was last seen winning a valuable handicap at Cheltenham on New Year's Day.
Williams said: "Aso has come out of his win at Cheltenham in good form and the Ryanair Chase is the target.
"He deserves his place in the race and it was a great performance to finish third in the Ryanair a couple of seasons ago and that is again where we will go.
"He will have possibly one or even two runs before the Festival. We could take him back to Cheltenham for Festival Trials Day (26 January) or go to Ascot for the Ascot Chase