The Poland international has insisted the club went back on its word and that he also feels "cheated" out of a move to Bayern Munich, which has admitted strong interest in the striker this summer.
However, with the new season approaching and with the 24-year-old still with a year to go on his contract, Klopp says it is time to end the saga and focus on the coming campaign with Dortmund.
"Whatever is left to be discussed will be discussed internally," the 46-year-old told reporters.
"The idea is to close this subject. Everything is in order. Nothing has changed since yesterday or the day before yesterday.
"I am convinced we will clear up everything in the coming days."
The striker became the first ever player to score four goals in a Champions League semifinal last year as BVB beat Real Madrid 4-1 in the first leg at Signal Iduna Park.
His prolific goalscoring exploits were not confined to European football, however, as he scored another 24 goals in the Bundesliga - coming second to Bayer Leverkusen's Stefan Kiessling in top scorers' chart.
Despite the summer rift, though, Klopp is not concerned that it will have a detrimental impact on Lewandowski's performances for die Schwarzgelben.
He added: "For me what he does [on the pitch] is a thousand times more important than what he says, because, what he does needs no interpretation."
Dortmund kicks off its Bundesliga campaign against Augsburg on Aug. 10, but faces Wilhelmshaven this Saturday in the DFB-Pokal first round.