Into Overdrive was beaten a length by eased-down Cheltenham Gold Cup hope L'Homme Presse in the Rehearsal Chase at Newcastle in November.
Mark Walford's improving stayer backed up that run when beating Sounds Russian by half a length in Wetherby's Boxing Day feature, taking his tally to five wins from eight starts over fences.
Walford feels the 142-rated stayer is nearing his prime and considers him nicely handicapped should he take his chance in the Aintree spectacular.
"We are in discussions at the moment, deciding whether we might run him in the National or not," he said.
"He is off a perfect handicap mark and a lot of previous winners were around the same mark. Emmet Mullins' horse won it off 148 last year.
"We are certainly not decided on that by any means, but it is one of the races we are thinking about. Otherwise it might be the Ultima at Cheltenham."
The Sky Bet Handicap Chase at Doncaster on January 28 is one option for the Wendy Hamilton-owned Into Overdrive.
Walford said: "We will look at the Sky Bet at the end of January, which is the next logical race. If we are going to go for the National, which is very much 50-50, we will not run until the weights come out."
Into Overdrive has looked highly progressive since winning a novice handicap chase at Carlisle in March off a mark of 112.
Having gone clear four out under Jamie Hamilton in the three-mile Rowland Meyrick, he had just enough to fend off Sounds Russian.
Walford feels he still has to improve plenty to be thought of in terms of a Gold Cup contender, however.
"He is going the right way and is a very tough horse," added the Sherriff Hutton handler. "He goes on any ground and distance is not particularly important. He can win from two and a half miles to three miles and maybe further.
"He has a lot to find to become a Gold Cup horse. There would not be many people putting Sounds Russian forward as a real Gold Cup contender and off level weights we wouldn't be beating him.
"He needs to improve a lot. He needs to find at least 15lb to be a Gold Cup prospect.
"He is certainly in his prime. We will see how we go, but I would imagine we would be sticking to handicaps for the time being."
