Permian will run for a seventh time this season if trainer Mark Johnston decides to give the Royal Ascot-winning colt the go-ahead in the Coral-Eclipse at Sandown.
The Middleham handler had been cool on sending the tough son of Teofilo back into action so soon after he thrived in the King Edward VII Stakes at the Royal meeting on June 23.
Permian has been on the go since April and won the Dante at York before finishing down the field in the Derby at Epsom.
Johnston said: "We've left him in and I wouldn't rule it out.
"The horse is well. It does come quickly (after Royal Ascot) but we said that last time, after the Derby."
Fellow Royal Ascot star Barney Roy seems likely to take his place in the Group One - even though he has never raced over the Eclipse trip of a mile and a quarter.
Trainer Richard Hannon has also given the St James's Palace Stakes winner the option of running in the one-mile Prix Jean Prat a day later at Chantilly.
But Hannon t old the Telegraph: "I'm favouring the Eclipse.
"He doesn't need any work and has come out of the St James's Palace great.
"I can't say I'm very confident he'll get a mile and a quarter, but there's every chance.
"He has always run to the line over a mile and is out of a Galileo mare."
Silvestre de Sousa is delighted to have been given the ride on leading Eclipse contender Eminent.
Martyn Meade's Craven winner has finished sixth in the 2000 Guineas and fourth in the Derby but the trainer has decided to replace regular pilot Jim Crowley with the title-chasing Brazilian.
"He's a nice horse, like everyone knows," said De Sousa.
"He won the Craven, he ran really well in the Guineas and ran well in the Derby. I'm delighted to have got the ride on him.
"It looks like he'll go there with a chance."
Aidan O'Brien has won the Eclipse on five occasions and has five contenders for this year's renewal.
The chief hope for the Ballydoyle handler appears to be Derby runner-up Cliffs Of Moher.
O'Brien told At The Races: "We're very happy so far. This will be a big week for him, but so far, so good.
"We've been very happy with him since Epsom."
