The four-year-old, who was a sensational winner of both the Commonwealth Cup and Haydock Sprint Cup last term, has endured a troubled campaign in 2017, with just one unplaced back at the Merseyside venue on her CV this year.
Quiet Reflection is reported to be firmly on the comeback trail now and while she could try to defend her Haydock title next month, Burke is considering other options should that outing not happen.
He said: "I am really pleased with her. She started cantering this week and she honestly looks the best I have seen her this year.
"We've got four weeks until Haydock and I'd like to run her there, but if the ground was good or quicker we might look for something else between then and the British Champions Sprint, or head straight there.
"She's been walking and trotting for a while and her overall level of fitness is pretty good. She's a dual Group One winner who has shown before what she can do at the top level."
Quiet Reflection is one of the headline names entered for the Qipco-sponsored event on October 21, with Diamond Jubilee Stakes victor The Tin Man in the mix to defend the title he won last year.
Trainer James Fanshawe said: "The Tin Man is in great form and he will be aimed at the British Champions Sprint. Hopefully we can have him in as good a form as he was last year when we get to October 21.
"It's a great day and we really enjoyed last year. He seems fine after Newmarket (eighth in the July Cup) and the idea is to aim for the 32Red Sprint Cup at Haydock next month."
Growl was a 50-1 chance when chasing home The Tin Man in last year's race and Richard Fahey is already eyeing the contest again after his charge's latest fourth in the Stewards' Cup.
"I thought he ran OK at Goodwood and hopefully he is on the way back," said Fahey.
"We had a great day last year on Champions Day with Ribchester also running so well and the prize money is so generous that you have to look at these kind of races.
"I've also entered Kimberella, who has been a brilliant little horse since he came to us, and Don't Touch, who was fifth last year, and came back with a little problem from his latest run at Newcastle. He's back in work again now though and I hope you'll see a much-improved performance next time."
Also entered are July Cup hero Harry Angel, Commonwealth Cup victor Caravaggio and dual Group One winner Limato.