"Every time you put opposition in front of him he beats them and is an absolute tip-top horse," Smith said.
"But we've left him on 135, which was the mark we had him performing to in the Irish Champion Stakes."
In showing his great turn of foot under Mick Kinane, sealing his sixth Group One in as many months, Sea The Stars became the first horse to win the 2,000 Guineas, Derby and Arc.
Though he is an odds-on favourite for next month's Breeders' Cup Classic, the Christopher Tsui-owned colt's stud value is already at an estimated £50million and it will be a surprise if he runs at Santa Anita.
"We'll let the dust settle and have a think about it and we're not ruling it out," said Oxx. "We're not going to rush into a decision and we'll have a discussion about it."