The John Smith's Grand National hero is available at around the 16-1 mark for the blue riband after finishing a tired second to Beef Or Salmon in the Hennessy Cognac Gold Cup eight days ago.
"We haven't made a decision and it is unlikely we will make a decision this week as we haven't put a time limit on it we will just see how things go," said Mullins.
"He didn't eat up on the evening after the race, but has been eating well since and is in much better form I am much happier with him."
Hedgehunter's defeat in the Hennessy followed on from his fourth place in the Lexus Chase over Christmas, which was his first outing over fences since his runaway success at Aintree 12 months ago.
The Trevor Hemmings-owned gelding is a leading fancy for this year's renewal of the National, with Coral quoting him at 10-1.
Meanwhile, Sadlers Wings will miss the Smurfit Champion Hurdle after aggravating an old injury.
The Willie Mullins-trained eight-year-old put in an eyecatching display in the AIG Europe Champion Hurdle at the end of last month when staying on strongly to finish fourth behind Brave Inca.
The gelding had been off the track since May 2004 before then with a suspensory ligament problem and was a 25-1 chance for the Festival.
"Sadler's Wings is out of the Champion Hurdle as he has an occurrence of his old injury," said Mullins.
"It only happened over the weekend and he won't make Punchestown either."
Sadler's Wings, winner of four of his seven starts over timber, landed his biggest career success when taking the Grade One Champion Novice Hurdle at the Punchestown Festival in 2004.
An unprecedented 1034 entries have been revealed for the 10 handicap events at the Cheltenham Festival.
The William Hill Trophy Handicap Chase has attracted 104 entries, including 19 possibles trained by Martin Pipe.
Therealbandit, Jaaci and It Takes Time could represent Pipe, while the 16 Irish-trained possibles include Robin Cook Memorial Gold Cup winner Sir Oj, dual totesport Cheltenham Gold Cup third Harbour Pilot and the Tony Martin-trained Dun Doire.
Last year's winner Spot Thedifference is among 44 entries for the Sporting Index Handicap Chase, which was added to the Festival line-up in 2005.
The Fred Winter Juvenile Handicap another new addition last year has attracted 90 four-year-olds.
The Coral Cup has the biggest entry of any of the handicaps with a record 151 horses going forward, including last year's winner Idole First.
Juveigneur is also bidding for back-to-back Festival victories and he is one of 124 entries in the Fulke Walwyn Kim Muir Handicap Chase.
Foreman, Turpin Green, Star De Mohaison and Wild Passion are a few of the classy 90-strong entries for the second renewal of the Jewson Novices' Handicap Chase, while the Racing Post Plate formerly the Mildmay of Flete Handicap Chase has attracted 109 possible runners for the first renewal under its new sponsorship.
The Pertemps Final (Handicap Hurdle) has a record 79 entries, while the Johnny Henderson Grand Annual Chase has 84 entered, including six trained by Nicky Henderson whose father is remembered in the race title.
The 2006 Festival is set to end on a competitive note on March 17 with the Vincent O'Brien County Handicap Hurdle, which has reeled in 131 horses at this stage.
Punchestown's chase track has been found unfit for racing and the two chases scheduled for Wednesday's meeting have been abandoned, with the remaining five races being divided to form a seven-race programme.