With 51 goals conceded in 38 games this season, reinforcements at the back are being sought at Upton Park.
It has not taken long for Rudiger to be identified as a top target and for an approach to be made.
A product of Stuttgart's academy system, the 21-year-old has enjoyed a standout 2013/14 campaign and earned a first senior international cap for Germany in a 0-0 draw with Poland on Wednesday.
His talents have now been noted by a number of sides, with West Ham believed to be heading a queue which includes Newcastle United and Schalke.
A £5million bid is believed to have been put to Stuttgart, with £2m worth of add-ons included in an effort to sweeten the deal.