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.
"There is no ultimatum for Ilkay Gundogan about a contract extension," Watzke said.
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."
