Permian is one of two horses supplemented for the Juddmonte Grand Prix de Paris on Friday.
The dual Group Two winner was added to the Group One field on Tuesday along with Italian Derby hero Mac Mahon, trained by Stefano Botti.
Connections of Permian are hoping it will be a case of second time lucky at the top level after the Mark Johnston-trained colt flopped in the Investec Derby.
He had been supplemented for the Premier Classic after winning the Dante Stakes at York and while he disappointed at Epsom, he showed his true colours when landing the King Edward VII Stakes at Royal Ascot.
"Permian is in very good form and we have half an eye on the Grand Prix de Saint-Cloud," Johnston's son and assistant, Charlie, told At The Races.
"It's a half a million euros Group One, so it would be a fantastic race to win. He's won the two best Group Two for three-year-olds so the natural progression is to go back into Group One company and it looks quite an attractive option."
John Gosden has left in Weekender, who represents the race sponsors as he is owned by Khalid Abdullah. The son of Frankel has had just the four starts and would be taking a big hike from handicap company. The owner also has Prix Hocquart scorer Ice Breeze, trained by Pascal Bary.
Aidan O'Brien has left in Orderofthegarter, Venice Beach and Spanish Steps after taking out Finn McCool.
Others in the frame are the Alain de Royer-Dupre-trained pair of Shakeel and Valamaz, Nicolas Clement's Falcon Wings and the Andre Fabre-trained Parabellum, who is owned by Godolphin.
