The John and Thady Gosden-trained five-year-old enjoyed a spectacular campaign last year, winning the Saudi Cup in Riyadh, the Dubai Sheema Classic at Meydan and the Juddmonte International at York.
Mishriff has thus far failed to add to his tally in 2022, but finished second in both the Eclipse and the International, as well as placing third in the King George and fourth in the Irish Champion Stakes.
The five-year-old got stuck in the mud in ParisLongchamp over the weekend and is due to commence stallion duties in France next year - but a trip to Kentucky next month remains on the table.
Ted Voute, racing manager to Mishriff's owner, Prince Faisal, said: "He's arrived back home and has eaten up. After I saw him in the unsaddling enclosure, we spent 20 minutes showering him off and he still had mud all over his head!
"You get the draw of 17 and the extreme ground, which I knew he didn't particularly like, but he came back safe and sound.
"Sumbe have now acquired the stud rights and we're still considering the Breeders' Cup. We're getting our thoughts together and ultimately John Gosden will make that call.
"John has mentioned the Breeders' Cup Turf many times throughout the year and I think, if we weren't going to do any harm to the horse, we might have a crack at it.
"It's too early to commit to saying that's what we're going to do, but he is back in the yard and hasn't gone straight to stud, so we've given ourselves a bit of a chance to have a look and a think.
"He loves travelling and looked a million dollars on Sunday."