Nick Scholfield put Irving through his paces on Monday morning ahead of a possible outing in this weekend's Sky Bet Dovecote Novices' Hurdle at Kempton.
The ride on the Supreme entry became Scholfield's after partnering him to victory on his British debut at Taunton before they followed up on two occasions at Ascot.
On the most recent, in the Mitie Kennel Gate Novices' Hurdle on 20 December, Irving gave subsequent Betfair Hurdle winner Splash Of Ginge 3lb and beat him by over six lengths.
"I schooled this morning, we just went around the arena and jumped a few hurdles," Scholfield told At The Races.
"He's really fresh and well and he might take his chance on Saturday in the Dovecote.
"His form is good and certainly in my mind he's probably best of the English novices so far this season.
"He has to be up in the betting for the Supreme."
Irving could face as many as 10 rivals and Nicholls has also entered Fascino Rustico.
Among the interesting contenders are Alan King's First Mohican, who was smart on the Flat with the Cecils and struck on his jumping debut at Doncaster.
John Ferguson could run either Dubai Prince or Mijhaar, both of whom were useful on the level, while Vaihau, Germany Calling and Garde La Victoire also catch the eye.
Nicky Henderson's Cup Final has not been seen since chasing home Irving at Taunton while the Nick Williams-trained Amore Alato is already a course and distance winner.