Permian appears increasingly likely to head America in a bid to open his account at the highest level in next month's Secretariat Stakes at Arlington Park.
After winning the Dante Stakes at York, Mark Johnston's colt disappointed when supplemented for the Epsom Derby, but showed his true colours with victory in the King Edward VII Stakes at Royal Ascot.
He returned to Group One level in the Grand Prix de Paris at Saint-Cloud earlier this month and was beaten just a nose by Shakeel after a pulsating finish.
Connections considered a tilt at Saturday's King George VI And Queen Elizabeth Stakes, but elected to sidestep Ascot in favour of a potentially easier option stateside on August 12.
Charlie Johnston, assistant to his father, said: "We'll have a look at how the Secretariat Stakes is shaping up and we'll have to make a decision one way or another by the middle of the week, as if he is going to run, he'll need to leave on Friday.
"He's in great nick at home. It's almost unbelievable, but he actually came out of the race in France better than he's come out of any race.
"If he'd won in France, we'd have probably run him in the King George and gone on to the Juddmonte International and the Arc. We could have rolled the dice.
"But obviously the main thing we need to try and achieve is to make him a Group One winner.
"If we have to travel to do that, we will do."