The six-year-old, trained by Alan King, earned £34,000 for winning the Kingwell Hurdle, which would more than cover the £20,000 needed on March 7 to add him to the field for the two-mile showpiece the following week.
Elgin had his first experience of Cheltenham last March when seventh in the Supreme Novices' Hurdle and returned to Prestbury Park to win the Greatwood Hurdle in November.
Dan Downie, racing manager for owners Elite Racing, said; "We thought he'd probably come on a bit having had a break after Ascot. He had been in very good form at home but we knew it was going to be tough with a penalty. We were really chuffed with the way he did it.
"We'll definitely have a look at supplementing him for the Champion Hurdle. We don't have to to anything until March 7. We'll see how he is, but I imagine that would be the route we'd go down.
"He's done nothing but improve and he likes the track, which is a big plus.
"He would have learnt a huge amount in the Supreme last year, which was a bit of a culture shock for him. They can go one of two ways after that and he's gone absolutely the right way, learnt from it and manned up.
"His jumping has become a lot more slick. He's just coming into himself, which is great."
Elgin is a 25-1 shot with William Hill for the Champion Hurdle on March 13.
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