More Of That is "very much odds against" running in the Ladbrokes World Hurdle at the Cheltenham Festival on 12 March, according to regular jockey Tony McCoy.
Jonjo O'Neill's seven-year-old defeated top Irish mare Annie Power in the race last season, when ridden by Barry Geraghty, but was comprehensively beaten upon his return to action at Newbury in November and has not run since.
The JP McManus-owned More Of That also bled after exercise last week to leave connections chasing the clock in order to prove his fitness for the Festival.
McCoy blogged on thejockeyclub.co.uk: "Sadly, More Of That bled in his work last week, which is hugely disappointing. Whether he gets back in the given time is very much odds against at the moment."
The 19-times champion jockey snubbed More Of That in preference for At Fishers Cross in last season's World Hurdle, but he could only finish third.
Rebecca Curtis' stayer has struggled this term, with McCoy distinctly nonplussed by his no-show at Haydock last Saturday.
He said: "At Fishers Cross ran deplorably bad at Haydock over the weekend - that is the only way of describing it - and he is long way off being a World Hurdle contender at the moment."
Paul Nicholls is happy with Zarkandar, who finished fourth last year, and Saphir Du Rheu in what he believes is an open year.
"Zarkandar is in really good form," the Ditcheat handler told At The Races. He won the French Champion Hurdle then ran really well at Ascot.
"Saphir won the Cleeve, which is always a good trial, and is an improving horse. It's a very open race. We've trained Zarkandar particularly just for this race. We haven't run him all year to keep him fresh and he's in good form.
"I think both horses have got big chances."