Tiger Roll -- the winner of the last two Grand Nationals -- is a long shot to run the race next year, according to the horse's owner Michael O'Leary.
The 4-1 favourite became the first horse since Red Rum in 1974 to win back-to-back Grand Nationals when he cruised to victory at Aintree on Saturday, and would become the first horse in the race's history to win three titles in a row if he were to win again next year.
Red Rum, who is considered the greatest horse in British racing history, won consecutive Grand Nationals before adding a third title in 1977, but O'Leary was doubtful that Tiger Roll would go for a historic third in 2020.
"It's very unlikely that he'll come back and run in it again next year," O'Leary told Racing TV.
"There's no reason to emulate Red Rum's feat of three wins. Tiger Roll isn't Red Rum -- he's Tiger Roll -- and I feel no pressure to go back and try to win a third time.
"There's huge public affection for him and I think we're duty-bound to mind him now."
While Tiger Roll triumphed, the steeplechase saw its first death in seven years with the loss of Up For Review, who was unable to stand after falling badly at the first hurdle.
The horse's death marked the first fatality at the festival's flagship race since the death of Synchronised in 2012, although a total of three horses died across the three-day meeting at the Liverpool racecourse.
O'Leary does not want Tiger Roll to suffer the same fate.
"He will be carrying top weight [next year]. He is a small horse and every time he runs now I get nervous. I'd hate for anything unfortunate to happen to him while he's racing.
"For his sake and for the sake of the race, I really wouldn't want to bring him back shouldering huge lumps of weight.
"He's loving the good life -- eating, drinking and sleeping."
As a result of the fatalities over the weekend, many viewers have threatened to boycott future Grand Nationals, and horse racing chiefs have vowed to hold a review.
A spokesman for the British Horseracing Authority said: "There's a level of risk involved in any activity in which horses take part. We work hard as a sport to keep those risks to a minimum and remove avoidable risk.
"We will take a measured, evidence-based approach to assessing the incidents, which will include reviewing video footage of all incidents and working with jockeys and trainers."