Recent speculation has linked Gundogan with a move to La Liga, with Real Madrid billed as favourites to capture his signature.
Spanish reports suggest Real view Gundogan as the ideal replacement for Xabi Alonso at the Bernabeu.
However, Watzke quashed the rumours, claiming what is written in the media cannot always be trusted and insists the Germany international has shown no desire to leave the Bundesliga club.
"If we believe all those stories from Spain in terms of which player is to leave our club, we would have trouble picking a proper team," he told German newspaper BILD.
"Neither Ilkay nor his father have yet told us anything about leaving."
Gundogan's agent, his father Irfan, concurred and claims that, with the player's current contract expiring in June 2015, talks with Dortmund over an extension will be the first port of call.
Speaking to German news agency Deutsche Presseagentur, Irfan Gundogan said: "Borussia Dortmund will remain our first partner of conversation when it comes down to discussing the future of Ilkay."
Gundogan has been limited to just 57 minutes of Bundesliga action this term after sustaining a back injury during an international friendly in August.