Eclipse winner Ulysses will be dropped back in trip on his next start in either the Juddmonte International at York or the Qipco Irish Champion Stakes at Leopardstown.
While a second shot at the Breeders' Cup Turf remains the long-term target for the Sir Michael Stoute-trained four-year-old, connections are weighing up which 10-furlong Group One contest he will take in next.
After claiming his first top-level success at Sandown last month, the son of Galileo found only Enable too strong when stepped back up to a mile and a half in the King George VI and Queen Elizabeth Stakes.
Alan Cooper, racing manager to owners the Niarchos Family, said: "We are going to have a chat with Sir Michael Stoute later this week and the plan for him will then become much clearer.
"He ran a super race in the King George, but he just met a very good filly.
"We just like to give the horse plenty of time to see how he is. He is in good form, but we would just like to wait a few days to decide if we go to York or Leopardstown.
"They are the two obvious options for him in August and September, then we will have a chat and re-group after that. All being well, the Breeders' Cup is the long-term plan again."