The 26-year-old defender is out of contract with Hertha Berlin at the end of the season and has been linked with a move to the Premier League.
West Ham have held talks with the German centre-back over a move to the London Stadium in the winter transfer window.
David Moyes is looking to bring in a centre-back in January after losing Angelo Ogbonna and Kurt Zouma to injuries and Stark is a top target for the Hammers.
But according to German magazine Sport Bild, the Hertha Berlin defender has also popped up on the radar of Bundesliga giants Dortmund.
BVB are in the market for a centre-back as well and Stark is a player the club are closely tracking.
His contractual situation at Hertha Berlin makes him an attractive target but it is unclear whether they want him in January or want to wait until the summer to snap him up on a free transfer.
West Ham are closely monitoring Stark but they are set to face competition from German giants Dortmund for his signature.
