The 24-year-old Poland international has long been linked with a move to the European champions, while Manchester United were also reported to be interested in his signature.
"I think it is a known fact that Robert is going to play for Bayern after the upcoming season," Klopp told Welt am Sonntag. "Now the only question is how to shape the time until then.
"That is our concern and it is our commitment to our fans and members to ensure that we will have a more competitive team in the upcoming season."
Lewandowksi, who scored 34 goals in all competitions last campaign, joined Dortmund from Lech Poznan in 2010.