Speaking in his Sporting Index blog, the big-race jockey confirmed the Clarence House Chase at Ascot to be the six-year-old's next likely port of call, while suggesting by the end of the season he could be classed among some of the great chasers of the modern era.
Defi Du Seuil - winner of the JLT Novices' Chase at Cheltenham in March - has won his two starts so far this season, beating Politologue in the Shloer Chase before lowering the colours of the evergreen Un De Sceaux in last Saturday's Betfair Tingle Creek Chase at Sandown.
Geraghty said: "I thought it was a very good performance, but there’s still more improvement to come which is the exciting thing about him.
"He travelled brilliantly and jumped pretty well, though he did get in close to the water and the ditch but I think he can only get better.
"I had to ask him a few questions a long way out and he picked up really well, while he showed a great battling mentality to get up and beat Un De Sceaux, who’s one of the best two-milers about.
"I’ve ridden the likes of Sprinter Sacre and Moscow Flyer before and I think Defi could be on his way to the very top.
"There’s no doubt he has the pace and he could continue to do well in the two-mile division, though he’s proved he can stay further too.
"The Clarence House at Ascot could be next and I don’t see why he wouldn’t continue to go for the big two mile races after last Saturday’s performance, but we’ll take it race by race."
Looking ahead to Friday's rides on day one of the International Meeting at Cheltenham, Geraghty said: "Chantry House in the opening novices’ hurdle (12:10) is one my two rides and he’d probably be my best chance of a winner on the day.
"He was a good point-to-point winner in 2018 and then followed up by winning a nice bumper at Warwick on his first start under rules last spring.
"He’s a horse that Nicky [Henderson] thinks a lot of and we were delighted with the way he won his bumper. The form of that race is working out really well and we’re hoping he can give a good showing. The ground looks set to be pretty testing but he’s a nice big staying type and I don’t see that being much of a problem for him."
On Never Adapt, he said: "She ran very free in Cheltenham last year and did very well to finish third considering how hard she pulled throughout the race. I know Nicky has always liked her a lot, but she really needs to learn to relax.
"If she does settle then the level of form from that race last year looks good and she’ll go well. The other thing is she’s been off the track for over a year as well, but fingers crossed she runs well. As I say, the yard think a fair bit of her, but the main thing is we need her to settle if we’re to have a chance."
