Adayar was a surprise winner of the Derby in June, but backed up that performance with a brilliant effort in the King George VI And Queen Elizabeth Stakes at Ascot.
Hurricane Lane, meanwhile, was third at Epsom and has since won the Irish Derby, Grand Prix de Paris and St Leger.
Appleby said the Frankel colts will work on Saturday, with a final decision due next week on Hurricane Lane's participation.
He told the Godolphin website: "A week is a long time in racing, particularly when you are coming into a race such as the Arc.
"We obviously have to take on board the well-being of both horses, but also the way the race is taking shape, and, very importantly, the ground at Longchamp.
"The one thing Hurricane Lane does not want is a quick surface. Adayar comes into the versatile category, but we have always felt ease in the ground enhances Hurricane Lane's prospects. Unfortunately, the weather in Paris is out of our hands.
"Hurricane Lane gallops tomorrow. Adayar will also gallop. Then there will be discussions with the team, and we will see where we stand during the week, whether we will have one or two Arc runners."
Of the decision Buick was facing, Appleby said: "It's a hard choice, but William is confident he's picking the right horse.
"I'm always happy for jockeys to be able to choose the horse they would like to ride. That means they have confidence in the horse and they take that into the race.
"James (Doyle) will partner Hurricane Lane in a simple piece of work tomorrow. Then discussions will take place next week on his participation.
"The exciting part is that it could be history in the making. Adayar has already made his mark becoming the first in 20 years to complete the Derby/King George double, while Hurricane Lane would be attempting something that's never been done, winning the St Leger and the Arc in the same year."
Appleby also picked out what he sees as the big danger to his runners – the Dermot Weld-trained Breeders' Cup winner Tarnawa.
He said: "Fillies at this time of the year, if they are going in the right direction, can be very hard to beat.
"Tarnawa is a Group One winner over course and distance (Prix Vermeille), she's a Breeders' Cup winner and finished a very good second in the Irish Champion Stakes. Her credentials are first class."