Lewandowski has been tipped to follow Dortmund team-mate Mario Gotze to the Allianz Arena this summer and one of his agents has claimed that talks are underway with Bayern.
The Poland international only has one season left on his Dortmund contract but Klopp currently expects the 24-year-old to return for pre-season training.
"As things stand, there is no official offer from Bayern Munich," the Dortmund coach told Bild.
"I expect Robert to be playing for us next season. We are going to ensure a line is drawn under the speculation in the coming days."
Klopp insists it would not be the end of the world if Lewandowski joins a Bayern side who beat Dortmund in Saturday's Champions League final at Wembley.
"We will see what happens. Anything is possible, but I can work with every scenario," he added.
"The only strange thing is that everybody is acting as if the issue has already been resolved.
"Jupp Heynckes says this, his agent says that - and we don't even have an offer for him. What's all that about?
"The way things are going is not very pretty."
Gotze, who missed the Champions League final through injury, will play for Bayern next season after the Bundesliga champions met the playmaker's release clause.