Bayern are reported to have already agreed personal terms with the Poland international but Bundesliga rivals Dortmund are refusing to sell him - a move that will cost the club millions in transfer income.
With only one year to go on his contract, Lewandowski can leave for nothing in a year's time and Rummenigge now expects that to happen.
"I assume they are quite aware of that in Dortmund," he told Sport Bild magazine.
"I get the feeling that (Dortmund general manager) Mr Watzke means what he says. He is bound to have considered very well his remark that Lewandowski has got to stay."
Dortmund last week said no official offer had been received from Bayern and they now consider the issue closed.
However, Rummenigge says the lack of a written offer does not mean they were never interested.
"That is not how things work in the football world," he said. "We did not send a written offer, but there are reasons for that and that does not change anything.
"We were prepared to sit down at a table with Dortmund."
That is now unlikely with Dortmund closing the door on any negotiations, even though their coach Jurgen Klopp admitted it is inevitable that Lewandowski will leave next summer.
"We now just want to prove that we can be successful next year with a quality player like Robert and I know that Robert sees things the same way," he said.
"Our results next season are more important than anything else."