Sir Michael Stoute says it is "very possible" Ulysses will tackle next month's Prix de l'Arc de Triomphe at Chantilly.
The four-year-old has really come into his own this season, winning both the Coral-Eclipse and Juddmonte International as well as finishing second to Enable in the King George at Ascot.
The Breeders' Cup Turf at Del Mar on November 4 was initially nominated as Ulysses' target following his York success, but Stoute has confirmed he may now stop off in France on October 1 on the way to his American date.
He said: "The Arc is very possible and we're aiming for that at the moment.
"The Breeders' Cup is not until five weeks after the Arc, so there's plenty of time between both races."
The impressive York winner is 7-1 for the Arc at Sky Bet.
Ulysses enjoyed a canter in front of the public on Sunday morning as part of Newmarket's Open Weekend and John Gosden also had his stars out in force.
Enable, who beat Ulysses by four and a half lengths at Ascot, is firmly on course for the Arc after her easy five-length victory in the Yorkshire Oaks last time out - her fourth successive Group One win.
Gosden said: "All being well, she's pointing for the Arc three weeks today.
"She's very relaxed in her work and everything she does. We didn't want to go from the King George straight to the Arc, so she went up there (York) and we were able to tick her over.
"She was forced to make her own pace, but she did it very well and she was a little bit bored in the last two furlongs. She took the race very well and quickly got back to her normal weight.
"We're now in the build up to the Arc and she will start doing some more important work this week."
Enable also cantered in Newmarket, following stablemate Cracksman up the gallop.
Plans for Cracksman are still up in the air following his wide-margin win in the Voltigeur at York and his impressive Prix Niel success at Chantilly last Sunday.
The three-year-old is entered for the Arc, but both Gosden and owner Anthony Oppenheimer have expressed their reservations about tackling the race this year.
Gosden said: "I do not necessarily want to commit to the Arc. If it was at Longchamp, I would probably not hesitate, but Chantilly is a very different track and possibly his Arc is next year, but no decision will be made until later on.
"He's in the Champion Stakes as well and he's already a winner over a mile and a quarter.
"The key thing about Ascot is the draw. You don't want to be drawn wide as it cost Jack Hobbs (when third in 2015) being drawn wide as a three-year-old.
"There are a number of decisions to be made, but I'll be in no rush."
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