Reports on Wednesday linked the Poland international with a move to the Bavarians, with Jupp Heynckes suggesting a deal was virtually agreed, while Goal.com understands Premier League champions United are pushing hard for the striker's signature also.
Lewandowski scored all four goals in Dortmund's thrilling 4-1 win over Real Madrid in the Champions League semi-final first leg on Wednesday night, and Watzke admitted that he would rather have the 24-year-old replicating that form at the Westfalenstadion next year and lose him for free than sell him now.
Watzke told ZDF: "I'm surprised [about the claims]. I don't know what agent Heynckes has. The fact is that Robert has a contract till 2014.
"Unlike Mario [Gotze] he has no release clause. We want Robert to play next year in Dortmund, for this we will 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."
Speaking to Sky Germany, Dortmund boss Jurgen Klopp added: "I don't believe Lewandowski is on the run. We won't send him away."
Despite the remarkable win over Jose Mourinho's men on Wednesday, Watzke insisted he was not getting carried away with the second leg at Santiago Bernabeu yet to come.
"I am very proud of the team," he added. "But I'm tense because I know the world will be another in six days."
Amid all the speculation regarding Lewandowski, the player himself refused to be drawn on the rumours linking him with Bayern and was adamant that his focus is firmly on Dortmund.
"I concentrate on Borussia," he told reporters. "We have important games in Champions League and Bundesliga, we have to see what happens then."