The Newmarket handler has claimed the one-mile Group One prize on a record five previous occasions and sees the Helmet colt as an ideal candidate for this year's renewal.
After striking at the top level in the Prix Jean Prat at Chantilly on his penultimate start, the three-year-old finished a close-up third in the Jacques le Marois at Deauville last Sunday.
Bin Suroor said: "Thunder Snow has been good after the race. He looks happy and fresh. The plan is to take him to the Queen Elizabeth II Stakes at Ascot.
"We will keep him only for that race. We will give him an easy time then get him ready for that race.
"He was so close to winning another Group One on Sunday, but sometimes it doesn't go your way."
A return to Germany could be on the cards for Betway Great Voltigeur entry Best Solution.
The son of Kodiac left behind disappointing runs in the Epsom Derby and in the King Edward VII Stakes at Royal Ascot when finishing second last time out in a Group One at Munich.
"He is entered at York and that is a possibility, but there are also different races in Germany for him. We will make a decision where he goes soon," the trainer added.