Premier League sides Arsenal, Manchester United, Chelsea and Liverpool have all been linked with the Germany midfielder, whose contract expires in June 2016.
Reports in the German press have indicated that Dortmund told Gundogan to sign a new deal or be sold at the end of the season.
However, chief exective Watzke has been quick to scotch those rumours.
"There is no ultimatum for Ilkay Gundogan about a contract extension," Watzke said.
Dortmund - who have finished in the top two in each of the previous four seasons - will resume Bundesliga action on January 31 in the relegation zone following a dreadful first half of the campaign.
Their poor form has led to pressure on coach Jurgen Kloop but, while Watzke conceded the former Mainz boss is unlikely to receive backing in the transfer market, he still has complete faith in his abilities.
Asked about the possibility of activity in the January transfer window Watzke added: "It is not very likely but not impossible.
"I still regard Jurgen Klopp as an excellent coach. [To think] anything else would be funny after the last six, seven years."
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
