So much so that Manchester United, according to local sources, slapped in an €18 million offer for the 23 year-old barely 24 hours after his header against Greece.
The speculation is unlikely to faze Lewandowski, however, who has been living with increased scrutiny regarding United ever since he struck a hat-trick in front of a watching Sir Alex Ferguson for BVB's German Cup final triumph over Bayern Munich.
"Since I started playing professional football, there has always been transfer rumours about me," said the Pole, who has a clear idea of how cut-throat professional football can be.
"I can't make a commitment to any club because I think that something like this in professional football is nonsense.
"Dortmund wants to keep me? Okay. But maybe someday they'll be desperate to sell. Then all their vows will not mean anything."
'Lewy' was making those comments in the middle of difficult contract talks last season with BVB. But his coach, Jurgen Klopp, insists the striker's influence off the pitch, his engaging, positive personality, went a long way to helping them achieve the Bundesliga and Cup Double last season.
"Clearly, the consultants play poker, the players do themselves a bit, but in the end, Lewy remains the same," smiles Klopp. "In football, the squad is a lot more than outsiders think."
Klopp is a huge fan of his centre-forward, as is Ferguson - and they're not alone.
Germany coach Joachim Low said of Lewy: "Lewandowski really impressed me. He's had a very good season. He is a guarantee of success for Borussia Dortmund."
Franck Ribery, the Bayern Munich winger, reckons Lewandowski "is more important" to Dortmund than the much-coveted Mario Gotze. While Lazio striker Miroslav Klose says: "I have followed his career, who in the past two years has improved considerably.
"His goal scoring record in the Bundesliga speaks for itself. You have to be a really good player to achieve those results in such a strong league."
Dortmund chief executive Hans-Joachim Watzke agrees: "We knew he was talented and capable of scoring goals at this level. But we didn't think he would develop so quickly and score with such consistency."
For all the protests from Watzke and BVB's directors, Lewandowski appears to have been preparing Dortmund fans for his departure this summer.
After clinching the Double, he confessed: "We have done it all this season. I've also thought: What can I now accomplish with Dortmund? What's left for me to do?"
Before leaving to join the Poland squad, Lewandowski even urged fans to read between the lines and understand Watzke's insistence that he wouldn't be sold.
"Mr Watzke has to say that," said Lewandowski. "For the moment, I'm the only striker Borussia has with Lucas (Barrios) now going to China."
If United is to be his next destination, the English giants will be signing a player convinced he's far from reaching his peak.
"No way!" protested the Pole when asked if he felt he'd fulfilled his potential.
"I will continue to grow, not only for the next two or three years, but much longer. I know that I still have a lot in reserve.
"Please remember that football is a game not just for your legs, but equally important, and at some level, more important, is the mentality."
Asked to describe himself, Lewandowski says his next club will be getting more than just a goal scorer.
"I'm more than a penalty box player. I usually create. I can work with the ball on the ground, play quickly on the counter-attack - my assists record is no fluke. I'm just a more versatile player."
"These are the players of the highest quality, it is difficult to compare in terms of achievement.
"Certainly in terms of value I am somewhat lacking, but ... I can achieve a lot by hard work in training. You can be sure I will be chasing Ronaldo and Messi. I can catch up!"