With the news on Monday that Frankie Dettori remains sidelined through injury, the plum ride aboard the John Gosden-trained son of Frankel is up for grabs in the Classic.
Owner Anthony Oppenheimer told Press Association Sport: "With Frankie injured I'm not sure who'll ride as yet. That's up to John."
Gosden was unavailable for comment, but a spokesperson for the yard said the Clarehaven handler will be looking for the "best available" jockey in the Irish Derby.
Olivier Peslier has not yet been approached, according to his agent, while Michael Haggas, the representative of James Doyle and William Buick, said on Monday he expects the two riders to be in action at Newmarket on Saturday.
Cracksman's unbeaten record came to an end in the Investec Derby, but he lost little in defeat when beaten a length in third, faring best of those runners who raced close to the pace.
Oppenheimer is hoping the colt can fly the flag for Britain "with distinction" in an international renewal of a race which Gosden won two years ago with Jack Hobbs.
And with Epsom hero Wings Of Eagles and French Derby runner-up Waldgeist lying in wait, a cracking race looks in store.
"The Derby form was given a few boosts at Ascot with Permian and Benbatl winning at Royal Ascot, which is always nice to see, and also the French form looks very good this year," said Oppenheimer.
"Mr (Andre) Fabre wouldn't be bringing Waldgeist over if he didn't think he'd be extremely competitive.
"I'm hoping we can fly the British flag with distinction."
After a resurgent week at Royal Ascot, Godolphin appear unlikely to be represented in the Classic.
Godolphin still have numerous options before Tuesday's forfeit stage, but they include the likes of Best Of Days and Best Solution, who both ran at Ascot.
There are also no plans to supplement Dubai Thunder, who finished down the field at Epsom.
"It's unlikely we're going to have a runner, I'd say," said Godolphin chief executive Joe Osborne.
"I don't think there are any plans to supplement anything at this stage.
"Permian and Benbatl won't go, we're just assessing all the options for them at the moment."
Bookmakers Sky Bet quote Cracksman and Epsom conqueror Wings Of Eagles as the joint-favourites at 9/4 in their market on the race.
