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The 12-year-old, who has fallen at the third-last in the blue riband for the last two seasons, also holds an entry the day before in the Ryanair Chase, which he won in 2013.
After being held by Bristol De Mai in the Betfair Chase at Haydock in November, the nine-time Grade One winner showed he still retains plenty of ability when pushing Waiting Patiently all the way in the Ascot Chase on Saturday.
Tizzard said: "Despite everything said about him over the last three months, he looks to be equally as good as he has ever been.
"We watched a recording of it (Ascot Chase) yesterday and he was only half a length down when he definitely got interfered with. I'm not taking anything away from Waiting Patiently as he won on merit on the day.
"Whether he goes for the Ryanair or Gold Cup, if you read Monday's paper it was all decided but it is not. We will let that run for a while.
"Jean (Bishop, owner) is coming down for three days to have a little holiday with the family and we will make a decision then for sure.
"There is no reason why we shouldn't go for the biggest one. Is that harder to win than the Ryanair? Possibly, yes."
The Milborne Port handler is confident Native River can reap the rewards of having a light preparation and better last season's third place.
Having missed the first half of the campaign, the eight-year-old made a winning return at Newbury earlier this month, when landing the Denman Chase for the second year in succession.
Tizzard said: "He came back in August, but we didn't want to put that leg under any more pressure than we needed.
"We spoke in depth all summer with Garth and Anne (Broom, owners) and we just wondered all year whether if having him ready in November for the Hennessy, the Welsh National, then the Denman, whether we had taken the edge off him a bit.
"We are a lot stronger this time round. He has just had the one run, but we had him ready at Christmas to run.
"He was equally as good (at Newbury) as he had ever been. He has got a wonderful chance. I think at the moment we have got it dead right with him. We've had a little skirmish round Newbury and sprinted for half a mile up the run-in over the last three fences, and that should put him spot on.
"He was ready to run first time, but he is bound to improve, as every horse does.
"How much he has got to improve, we will find out."
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