David Hayes is a step closer to crossing another item off his bucket list with Criterion a possible contender in Europe's most prestigious race, the Prix de l'Arc de Triomphe.

Hayes' co-trainer Tom Dabernig said the four-year-old, who is at Newmarket preparing for the Prince Of Wales's Stakes at Royal Ascot on June 17, would be nominated for the Arc in October.

"It would be great for the business to be represented there, Dabernig said.

"As David says it's on his bucket list to have a runner in the Arc."

Dabernig said the stable was not getting too far ahead of itself but was formulating a program to target the Arc.

He said depending on how Criterion performed in the Prince Of Wales's Stakes, the Juddmonte International at York on August 19 was on the agenda.

Criterion took a few days to recover from his trip to Newmarket after running third in the QEII Cup at Sha Tin on April 26.

"He raced in Hong Kong on the Sunday and then left on the Tuesday for England so he had a bit of a hectic time," Dabernig said.

"We've now got a bit of time up our sleeve.

"He's at John Gosden's stable and David's son Ben is there and Roy McCormick, who travelled with the horse to Hong Kong, has gone as well.

"David's going over next week. He's going to China for a few days and then he'll go on to Newmarket to see the horse.

A run in the Arc would rule Criterion out of a Melbourne spring campaign as he would not have time to fulfil quarantine requirements.

Criterion has had five starts since joining the Lindsay Park team late last year.

He has been in the money each time with his shining moment victory in Sydney's richest race, the $4 million Queen Elizabeth Stakes in April.