The Polish striker was the hero for the German club as they defeated Real Madrid 4-1 in the Champions League semi-final first leg, scoring all four goals.
"I don't believe Lewandowski is on the run. We won't send him away," Klopp told Sky Sports.
Watzke told ZDF: "Unlike Mario (Gotze, who has signed with Bayern) he has no release clause. We want Robert to play next year in Dortmund, for this we waive a transfer fee.
"But first of all we have to talk with Robert. He is one of our most important players and a great guy.
"We have a good relationship and the transfer fee does not matter. I want him to stay, and in my life a lot of my wishes came true."