Zaha, 27, is looking to leave Palace and the London club are open to selling him for the right price.
However, a move to Dortmund is ‘extremely unlikely’ according to Germany’s Sky Sport.
Zaha has indeed been offered to Dortmund, but the Germans have not actively approached him.
The feeling is they have been name-dropped in response to rumours linking Jadon Sancho to Manchester United.
Sancho now seems likely to stay with BVB, making a move for Zaha seem improbable unless of a twist in the Sancho tale.
Zaha was priced out of a move to Arsenal and Everton last summer when Palace slapped an £80m-plus (€88.3m) price-tag on him.
Sky Sport suggests he could now be bought for ‘more than’ €30m (£27.2m) but considerably less than £80m.