The German defender has not yet recovered from the knee problem that forced his withdrawal against Sunderland while his team-mate has picked up a hamstring injury
Potters manager Mark Hughes confirmed that the central defender has been unable to train all week due to the knee injury that forced him off in the latter stages of November 23's 2-0 win over Sunderland.
Arnautovic, who played the full 90 minutes against the Black Cats, has been laid low with a hamstring problem, meaning that the Welshman will be required to tinker with his starting XI at Goodison Park against the club for whom he once played.
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"He's got a little bit of an issue that we're going to try and manage initially. Obviously, if that doesn't work he will probably need the knee seeing to.
"We're hopeful that, with the work that he's doing the medical team, we'll be able to settle it down and he'll be able to play again.
"Marko is also unavailable as he's got a hamstring strain that will keep him out for a couple of weeks."
Hughes, though, has received some good news in the build-up to his side's trip to Merseyside as midfielder Stephen Ireland is fit again following a shin injury.