Adayar is being lined up for a crack at The King George VI And Queen Elizabeth Stakes at Ascot in late July.
Runner-up in the Lingfield Derby Trial, the Frankel colt went one better at Epsom on Saturday under Adam Kirby - providing Appleby with his second victory in the premier Classic, following the success of Masar in 2018.
The Moulton Paddocks handler reports Adayar to have taken his exertions well and is hoping he can become the first horse since Galileo in 2001 to complete the Derby-King George double on July 24.
"He has come out of the race great," said Appleby.
"He went on the sea walker yesterday morning and he has been out for a jog this morning and has been turned out in the paddock, and he has shown his wellness. All signs are good so far.
"Without rubber stamping anything, the discussions taking place at the moment are that we will give this horse a bit more time and look towards going to a King George with him.
"I think timing-wise it suits him, and also we will have tested our mettle a bit against the older horses.
"After that we can see what he is like against the older horses, and if he happens to win a King George we can work back from an Arc. If he gets beat in a King George then we revert back to our original plan - which was going down the St Leger route.
"I think, personally, looking from the outside having won neither race, I would rather pinpoint one - because we all know in the autumn it is a big ask to do a St Leger and then an Arc."
Appleby has also begun making plans for Hurricane Lane and One Ruler, who finished third and sixth respectively behind Adayar at Epsom.
Hurricane Lane is bound for the Dubai Duty Free Irish Derby on June 26, while One Ruler could drop back in trip for the Hampton Court Stakes at Royal Ascot next week.
Appleby added: "I was delighted with Hurricane Lane. He was the horse I thought in the paddock looked magnificent - and I thought he took the preliminaries very well.
"What did surprise me, but we took it as a positive, is that he was very much learning on the job there. He showed his inexperience. Going into the Derby, I thought he was one run short of what I would have liked.
"I'm delighted with how he has come out of it, and the plan is to head straight to Ireland.
"We will drop One Ruler back to 10 furlongs. James (Doyle) said he didn't handle the track particularly well, but he didn't see it out either. We might look at something like the Hampton Court - we will see what his wellbeing is like.
"He would carry a penalty in that from his Autumn Stakes success, but we could look at something like that - or wait for an Eclipse."