The Quarterback needs to win The Goodwood impressively to be considered for Royal Ascot.
Trainer Robbie Griffiths favours a spell for the sprinter after he runs in the Group One race at Morphettville on Saturday.
"If he happened to win easily and pulled up well we might talk about it, but if I had to lock it in today I would say he will be off to the paddock," Griffiths said.
"I don't think he'll hold-up long enough to go across to England."
The Quarterback came up with gate one in Saturday's sprint and is a $13 chance behind the $3.80 favourite Black Heart Bart which drew barrier two.
Griffiths said the inside draw for The Quarterback was not ideal.
"It's going to create a few traffic issues," Griffiths said.
"It's not the perfect barrier for his style but it doesn't really matter.
"Wherever we go he's going to be in the same boat."
The Quarterback defeated Black Heart Bart and Chautauqua in the Newmarket Handicap then bungled the start when a closing fifth in the William Reid Stakes at Moonee Valley in March.
At his last start The Quarterback finished third behind Miss Promiscuity in the VOBIS Gold Sprint at Caulfield on April 16.
"He blew out a foot abscess about a week after that run and whether that affected him, I'm not too sure," Griffiths said.
"He's over it now, he galloped well today and seems fine.
"It's a question of whether he can return to the type of performance again that saw him run three peak performances in the Oakleigh Plate, the Newmarket and the William Reid.
"If he can then he's a super chance on Saturday."
Griante, winner of The Galaxy at Rosehill in March, is an early Goodwood scratching after pulling up sore following a gallop at Mornington on Tuesday.