Trainer David Wachman will keep options open for Galileo Rock following his fine effort in the Sandown Classic Trial.
Making his seasonal reappearance at the Esher course, Wayne Lordan's mount was third to Sugar Boy, beaten by just three-quarters of a length and doing his best work at the finish.
The colt holds big-race entries in the Investec Derby, Dubai Duty Free Irish Derby and at Royal Ascot.
Wachman said: "He seems fine after his Sandown run and travelled well. I'd like to think there's more to come as he was finishing best.
"He was very green and raw. He gave the front two a good start. He'll not go to Leopardstown at the weekend (Derrinstown Derby Trial) as that has come a bit quick for him. He'll keep working away and I'll keep an eye on everything. He's in the Epsom Derby, Irish Derby and French Derby."
Stablemate Duntle could go to Leopardstown, with the Amethyst Stakes a possible starting point for her four-year-old campaign.
Highly progressive last year, including in victory at Royal Ascot, the Danehill Dancer filly lost the Group One Matron Stakes in the stewards' room last September.
Wachman said: "She needs good ground and I hope to run her next Sunday at Leopardstown.
"Otherwise she could go for a race on Guineas weekend at the Curragh (Abu Dhabi Stakes).
"I think the good ground is coming and it's essential for her campaign, even though she was good in a Group Three on slower ground (Desmond Stakes at Leopardstown).
"Royal Ascot is definitely part of the plan for her."