The Schwarzgelben have denied the Poland international, whose contract runs out in 2014, a move away from Signal Iduna Park this summer, with the Bavarians having led the chase to sign the striker.
Klopp has accepted that it will be impossible to keep the 24-year-old from Bayern's clutches beyond the current season but is keen to make the relationship between forward and club work in the coming 12 months.
"I think it is a known fact that Robert is going to play for Bayern after the upcoming season," he told Welt am Sonntag. "Now the only question is how to shape the time until then.
|11/2||Borussia Dortmund are 11/2 wth bet365 to win the Bundesliga next season
"Up to a certain point we were with Robert's desire for change and were ready to talk. But nothing happened so we had to eventually say: '[A sale] now no longer works for us.'
"And now we want to prove that, with a quality player like Robert, we can be successful in the coming year. Our results in the coming season is what we're all about. I know that Robert and I see it the same way."
The BVB coach also revealed that Mario Gotze's €37 million [£31.8m] move to the Allianz Arena, which was agreed in April, was more upsetting than the club's eventual Champions League defeat to Bayern in the final.
"That was the bigger disappointment in the moment [than the Wembley loss]," Klopp added. "Mario was, until mid-April, a key part of our planning. And suddenly we were confronted with the reality that he wasn't.
"That was pretty tough. Basically, it is normal if a football club want to sign a player from another team. We do, too. But it was the timing of the notification of the transfer, the day before our important semi-final against Real Madrid, which was something disreputable. But, otherwise, there was little in the last season that was painful."
Despite Bayern's tendency to outspend Dortmund, Klopp is happy with how his side operate and favourably compared his side to English folk legend Robin Hood against the reigning German, DFB-Pokal and European champions.
"It will be infinitely hard [to win the Bundesliga this season]," he continued. "Bayern were quite possibly the best team in the world last season.
"But they did not beat us yet in the league on both occasions. And maybe we can also use the fact that we have not won anything in the last season, pulling against a certain power and greed.
"We have a bow and arrow. And if we aim accurately, we can hit them. Only the Bavarians have - I feel - a bazooka. The probability that they will hit us is so much larger. Nevertheless, Robin Hood is said to be very successful!"