Trainer John Gosden has stressed the five-year-old, who has also been given an entry in next week's Magners Rose Doncaster Cup, will only line up in the Group Two contest on October 19 if the ground is not too soft.
The son of Sea The Stars secured a second Weatherbys Hamilton Stayers' Million bonus last time out when adding to victories in the Yorkshire Cup, Ascot Gold Cup and Goodwood Cup in the Lonsdale Cup at York.
Gosden said: "I would think that Champions Day is quite likely.
"If we got a lot of rain and it did go heavy, that would be the one thing that would probably stop us running.
"He has got a great action and he is probably happiest on top of the ground. He handled the good to soft and softish ground, but I would be worried about heavy ground.
Having seen Stradivarius extend his winning sequence to nine on the Knavesmire on his most recent start, Gosden reports the talented stayer to have come out of the race in good shape.
Gosden added: "He is in tremendous form since the race. He is bucking and playing away and having a shout which he likes to do.
"He always lets you know when he is around. For a little guy he makes a lot of noise."
Looking beyond Qipco British Champions' Day, the Newmarket handler insists a decision whether Stradivarius stays in training next year will be made by his owner Bjorn Nielsen.
Gosden added: "It is very much up to Mr Nielsen whether he wants to keep him in training next year and I will leave that entirely to him.
"The horse is vociferous to let us know what he thinks."
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