Dunaden's next attempt to win a European Group One will come in the Grand Prix de Saint-Cloud on June 23.
The Mikel Delzangles-trained globetrotter famously won the Melbourne Cup in 2011 and followed up in the Hong Kong Vase.
He returned to Australia to win the Caulfield Cup last year but has always come up just short of the top level in Europe, most recently behind St Nicholas Abbey in the Coronation Cup at Epsom.
"Dunaden came out of Epsom fine. He's very well," Delzangles said.
"He'll run next in the Grand Prix de Saint-Cloud.
"I'm sure he's capable of winning a European Group One over a mile-and-a-half (2400m), one of them will be within his reach.
"I don't know about going to Australia again, we haven't decided yet and we won't until later in the year.
"At the moment it is possible he'll stay in Europe, but we'll see."