The 23-year-old has just over 12 months left on his current deal and a host of clubs from around Europe are being strongly linked with a move for the Germany international.
Manchester United are one of those reported to be monitoring his situation, but Dortmund are hopeful of agreeing fresh terms.
Gundogan is currently sidelined through injury and his father Irfan has stated that his main focus was on returning to fitness and sealing a place in Germany's World Cup squad.
But Dortmund want a new deal finalised before he possibly departs for Brazil this summer.
Watzke told Sport-BILD weekly: "Ilkay Gundogan is an important player of our squad we want to keep at our club.
"We have submitted a contract offer to Ilkay Gundogan and we are expecting to hear from him about it.
"And we are certainly not going to need to wait until the summer to see him reply."