Watch a full replay of the Betfred Dante Stakes won by Permian at York on Thursday and the reaction from winning trainer Mark Johnston and jockey Franny Norton.
"We're delighted with the two horses there. I've already spoken to Sheikh Mohammed and he is as thrilled as we are and is very keen to have this horse supplemented for the Derby.
"Permian will be supplemented. Saeed (Bin Suroor) had Best Solution win the Lingfield Derby Trial and Benbatl finished second in the Dante so we have to sit down, think, decide and talk to Sheikh Mohammed about that and what he thinks is the right thing to do."
Permian is now a best-priced 16-1 for the Derby with William Hill, behind 6-1 Cracksman and Cliff Of Moher.
Godolphin now appear to hold a strong hand for Epsom and Ferguson added: "With the way Benbatl has run on there, there's every chance (could go to the Derby). The Epsom Derby is the Epsom Derby.
"If you look at the form leading up into this race, there's a lot of respect for Aidan's (O'Brien) horse who won the Dee Stakes (Cliffs Of Moher) and he was followed home by Bay Of Poets, who wasn't far behind this horse and Cracksman at Epsom.
"Luckily there are still cards, not to play, but to analyse. It's just great to be in a season where so many three-year-olds have a live chance and no doubt in time we will find out exactly where they stand.
"If Churchill stays the mile and a half he is going to be a very tough nut to crack, but these horses all deserve to take their chances and it's just great to be going to the party."
Bin Suroor felt the runner-up would learn again for the experience.
He said: "I'm happy with that, he still needs more experience but he's learning all the time.
"He shows us he is a good horse at home. A mile and a quarter looks to be his trip, but we're still looking at the Derby as his aim, along with Best Solution. Obviously, Sheikh Mohammed will make the decision."
Stoute expressed doubts about Crystal Ocean's Derby claims before the race and when asked about Epsom, he said: "I wouldn't (run), but he has an owner that might want to."
Joseph O'Brien said of Rekindling, who was fourth: "He ran a good race, but he could have done with better ground.
"It's a bit early to say whether we'll go for the Derby after that."
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