Rajasinghe could step up to a mile at Del Mar next month in the Breeders' Cup Juvenile Turf.
Richard Spencer's charge won the Coventry Stakes at Royal Ascot before finishing third in the July Stakes at Newmarket, but was then off the track until reappearing in the Middle Park Stakes last month.
He finished 11th of the 12 runners that day but Spencer felt the good to soft ground had gone against his charge and believes a step up in trip combined with quicker going would be more in his favour.
The Newmarket handler said: "He could go to the Breeders' Cup meeting for the Juvenile Turf over a mile.
"I think the ground just wasn't quick enough for him at Newmarket last time.
"Back on faster ground and with a step up in trip, I think you would see a better performance as it just didn't suit him in the Middle Park.
"He's had a great season, though, so you certainly can't knock him for that run.
"You would expect the ground to be quicker in America, so that would be an option, but we won't make a decision until a bit nearer the time."