Lewandowski was the scourge of Real Madrid on Wednesday night, scoring all four goals in a wonderful individual display as Dortmund thrashed Jose Mourinho's men 4-1 in the first leg of their semi-final tie.
The 24-year-old is out of contract at the end of next season and has so far refused to commit to a new deal, meaning Dortmund must now consider whether to cash in at the end of the season or lose him for nothing in 2014, and Klopp told ZDF television: "I don't get the feeling Robert is on the run. We'll just have to see what happens."
Speculation in Germany has suggested Bayern Munich are leading the race to sign Lewandowski and pair him up once again with Mario Gotze, Dortmund's Germany playmaker who this week agreed a summer move south after Bayern met his release clause.
Bayern coach Jupp Heynckes' agent even claimed this week Lewandowski had an agreement in place with the Bundesliga champions but Klopp is willing to play the waiting game.
Lewandowski refused to discuss his future post-match but Dortmund general manager Hans-Joachim Watzke outlined the club's determination to keep him for another 12 months even if it means seeing him eventually depart on a free transfer.
"Our wish is explicit that he stays here," he told Sky television. "We will even do without receiving a transfer fee for him - that doesn't interest us in the slightest. Robert's contract runs until 2014 and, unlike Mario Gotze, there is no get-out clause."
Klopp believes Poland international Lewandowski on Wednesday night wrote his name into Dortmund folklore, adding: "Whenever I walk through the Borusseum (the club's museum), I always see the same old videos.
"Maybe now Robert's four goals will find a place in there, but for that to happen, we have got to build on this in the second leg."
Despite holding a handsome first-leg lead, Klopp insists his side will not sit back in next week's return at the Bernabeu, and he added: "We are not a team who can simply defend a result. We always want to attack. We have played an extraordinary game against a fantastic team, but nothing has been decided yet."
Source: PA
Source: PA