The Germany international is eager to leave BVB this month and a return to London for the former Chelsea striker is on the agenda, says BILD.
The player's advisor Ingo Haspel told Sky Deutschland: "Basically, André wants to play as much as possible.
"And if the playing time is not guaranteed, then it would be downright negligent not to think about what the future might look like and where to get more playing time."
Schurrle is an outside chance of making Germany's World Cup squad - but needs to be playing regularly to convince coach Joachim Low.
A move to West Ham would suit the winger - and it's understood BVB won't block any move if Haspel comes to them with an offer.