Speaking to Sky Sport Germany (h/t Charlie Malam of the Daily Express), Kovac hinted that while Lewandowski may want to go elsewhere amid ties with Real in particular, his current employers aren't ready to part ways:
"There's nothing new with Robert, it's clear that he will not leave this club because we have a top striker and we certainly do not want to relinquish him or give him away.
"We want to achieve a lot with him. He is a great footballer, who has achieved a lot in the Bundesliga, scored many goals and now in the new season certainly will score many goals."
"It's true that Robert toys with going elsewhere. Only [he has] one thing he likes, the other is what we like to do.
"Robert has a contract—I do not know how long—and he will certainly stay as long as possible here."
Kovac's comments came after Sport Bild journalist Christian Falk reported Lewandowski recently wanted showdown talks with the club regarding his stay at the Allianz Arena:
Malam's article also included quotes from Lewandowski's agent, Pini Zahavi, who said his client was open to a transfer away from Bavaria: "Robert feels he needs a change and a new challenge in his career. The managers of Bayern know about it. Robert's motives are not money or to join a specific club."
However, Marca's Juan Ignacio Garcia-Ochoa wrote that there is a specific club Lewandowski has in mind as he is "still dreaming of a move to Real Madrid," who are looking to bounce back from the sale of Cristiano Ronaldo to Juventus.
There's a galactico-shaped void at the Estadio Santiago Bernabeu, and although Karim Benzema, who is 31 in December, remains the central striking option at present, Lewandowski would be an upgrade.
There's other potential competition in the market, however, after Borussia Dortmund figurehead Hans-Joachim Watzke confirmed his old club would take him back if the chance arose, per Goal's Ronan Murphy:
Ronan Murphy @swearimnotpaul
Borussia Dortmund chief Hans-Joachim Watzke would love to bring Robert Lewandowski back, telling Sport Bild: "Robert knows the business, the league, even the club, and we know he would work right away, and for such a player I would be willing to pay €100m." #BVB #FCBayern
It's been four years since the Poland frontman departed the Westfalenstadion for Bayern, but at 29, it seems unlikely Lewandowski would look back instead of pursuing what could be the biggest move of his career.
The Bundesliga's top scorer in three of the last five seasons, Lewandowski has proved he's a world-class asset in Germany's top flight, although WhoScored.com noted there's room for improvement, too:
Speculation increased when Lewandowski left his agent of 10 years, Cezary Kucharski, to join up with Zahavi in February of this year, but Kovac and Bayern seemingly remain uninterested in selling.
Die Roten are no strangers to playing hardball on such matters, and with three years left to run on his contract, any hopes Lewandowski might have of switching to Real or United look unlikely to be met this summer.