The 23-year-old has been strongly linked with a move away from Dortmund as he is yet to agree a new contract with the club.
Arsenal and Manchester United are reportedly leading the chase for the £25million-rated ace.
Watzke said: “In the case of Ilkay Gundogan, we do not yet know how it will turn out. We would love to extend (a contract) with him.”
United boss David Moyes is desperate to strengthen his midfield in January and could make a move for Gundogan as well as Atletico Madrid starlet Koke, according to the Daily Star.
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After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.