The Poland international has been heavily linked with a move to Bundesliga champions Bayern Munich, who beat Dortmund to win the UEFA Champions League on Saturday at Wembley.
Lewandowski’s agent claimed on Monday that an agreement between the clubs was the only thing left to be done in the deal.
However, Klopp insists there has been no offer from the Bavarian club, and is keen to see the striker’s future determined shortly.
“As things stand, there is no official offer from Bayern Munich,” Klopp told German newspaper 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.”
Lewandowski has scored 24 times in 31 Bundesliga appearances this season, but Klopp believes it would not be a disaster if he were to leave, having previously replaced the likes of Shinji Kagawa and Nuri Sahin in his plans.
“We will see what happens. Anything is possible, but I can work with every scenario,” Klopp continued.
“The only strange thing is that everybody is acting as if the issue has already been resolved.
“(Bayern manager) Jupp Heynckes says this, his agent says that – and we don’t even have an offer for him. What’s all that about?”
Klopp confirmed after Saturday’s defeat that he would need to strengthen the squad ahead of next season and he has already been busy, bringing in 24-year-old defender Sokratis Papastathopoulos to the club from Werder Bremen.
The Greece international has signed a five-year deal with Dortmund and commented to the club’s official website: “I gained a lot from my two years with Werder but now I feel ready to make the next step.”
Heading out of the Westfalenstadion exit door is Felipe Santana, who has joined Ruhr Valley rivals Schalke.
The 27-year-old Brazilian had found his first-team appearances limited due to Klopp preferring a centre-back partnership of Mats Hummels and Neven Subotic.