Klose jarred his knee in last weekend's loss to Crystal Palace, and Sky Sports claim he has been absent from training all week.
The former Wolfsburg man has played 10 Premier league games for the Canaries since his arrival at Carrow Road in January.
The East Anglian outfit have been on a terrible run of form since the turn of the year, and it took Klose time to adjust to the rigours of English football.
After a handful of games, the big Swiss centre-back managed to acclimatise to the change, and has become an extremely important component in the Norwich team.
He has helped the Canaries achieve two clean sheets in their last four fixtures - games that have yielded seven points from a possible 12, and taken them four points clear of the drop zone.
Alex Neil and his side will be hoping for three points at home to the Black Cats to make their run-in that little bit easier, although he will be hoping that Klose's potential absence will not have an adverse effect on his side's chances of victory.