Joshua Tree could bid to end a successful season in the Hong Kong Vase in December following his victory in the Canadian International at Woodbine.
Trainer Marco Botti has ruled out a run in the Breeders' Cup at Santa Anita and the Japan Cup on November 25 is now looking doubtful.
Botti will monitor the globe-trotting five-year-old's condition over the next week before making a final decision on a trip to Sha Tin for the mile-and-a-half Group One.
"No Breeders' Cup for sure. Of the Japan Cup and Hong Kong, we are leaning towards Hong Kong now," said the Newmarket handler.
"That is the situation at the moment but we want to see how the horse is over the next week or so before we make the final decision.
"At this stage it is unlikely he will go to Japan while Hong Kong is the possibility.
"The horse came back on Saturday and he's well and is in good health."