Ryan Shawcross has failed to recover from his back injury in time and Geoff Cameron remains out with a thigh complaint.
The injuries are ill-timed for Stoke, as loanee Kurt Zouma is also unavailable for selection this weekend against his parent club.
Manager Mark Hughes said in his press conference on Friday morning: “We are struggling a little bit defensively, I have to say.”
On Wimmer’s ongoing battle for fitness, Hughes added: “That's touch and go. We haven't given up hope, he might be OK.”
What are Hughes' options?
That would leave Bruno Martins Indi as Stoke’s only fit senior centre-half. With the manager persisting with a back three so far this season, at least one player is going to find themselves in an uncomfortable position against the Premier League champions.
If Wimmer passes fit, Glen Johnson could be the logical choice to fill in alongside him and Martins Indi, though not a natural fit in the position. This week's cup exit was also Johnson's first competitive game of the season.
Hughes occasionally deployed Johnson in his central three last season, while experimenting with his formation. But Stoke often looked worryingly open at the back, form that prompted a flurry of defensive signings this summer.
Late arrivals in the transfer window were matched by late departures, too. Philipp Wollscheid left permanently for Metz in Ligue 1, while the popular Marc Muniesa went out on loan to Girona in La Liga. Now Stoke find themselves short of defenders only a month into the new season.
Hughes said: "We are struggling on the injury front at the back. Shawcross & Cameron are out, Wimmer is struggling & Zouma can't play against Chelsea."
One alternative for this weekend would see Erik Pieters tuck in from left-wing-back – but that would mean a league debut for 18-year-old Josh Tymon in his stead.
Though Tymon featured five times in the Premier League last season for relegated Hull City, Hughes may hesitate to throw his promising youngster off the deep end at this early stage of the season.
Should Wimmer be ruled out of the home match against Chelsea, Hughes faces little choice but to revert to a back four, still starting one player out of position.