Dortmund are understood to have already made contact with Zaha’s representatives as they attempt to find a replacement for Christian Pulisic, who joined Chelsea this month for £58 million (R1.04 billion) but will not arrive at Stamford Bridge until next season.
Despite signing a new contract at Selhurst Park at the start of this season worth £130,000 (R2.3m) a week that lasts until 2023, it is believed that the 26-year-old would be open to a move to Germany as he is keen to play in the Champions League.
The former Manchester United forward recently received a mouth-watering £44m contract offer from the Chinese Super League, but the club quickly dismissed the interest.
According to The Guardian, Palace are likely to demand a fee in excess of £50m (R900m) for the player.
BVB sporting director Michael Zorc remained mum when questioned about the interest in the Ivory Coast international.
"You must be here for the first time, otherwise you would know that we don’t comment on any transfers," he said at in a press conference today, as per Sky News. "I can only say he is a good player."
The German's side current transfer record is the €30m (R469m) they paid Wolfsburg for André Schürrle in 2016.
Although they have recouped more than £220m (R3.9bn) since August 2017 from the sales of Pulisic, Pierre-Emerick Aubameyang and Ousmane Dembélé.