The 29-year-old has been linked with a move away from the Allianz Arena after his agent said in May that the Poland international "needs a change".
But Kovac - speaking at his first press conference as Bayern boss on Monday - said he had spoken to Lewandowski and told him that he wants him to stay.
"Bayern Munich has a very strong squad, everyone's a class player," Kovac told the assembled media.
"I do want to keep the players here, but obviously I know things can happen in the transfer market. Currently, there's nothing to report.
"I was on the phone with Lewandowski and told him my opinion. I'm looking forward to working with him. He's a world-class striker who has achieved a lot at this club [and] in the future will continue to perform that way."
Kovac - who joined Bayern on a three-year deal from Eintracht Frankfurt - inherits eight players who formed part of the Germany squad that sensationally crashed out at the first-round stage of the World Cup for the first time since 1938.
While conceding that he is disappointed with the national team's shock early exit, he does not think it will have a lingering impact on his players when they return for pre-season training.
"It's annoying and frustrating that they're out of the World Cup," he added.
"As coach of Bayern Munich it's true that I'm quite happy about that because I have a few players that will join me sooner.
"The disappointment is there, but I think they will forget that on vacation. And I think that they will be fully motivated on the first day of training - I expect passion and ambition.
"These are players who can motivate themselves and want to win more titles despite many titles [already]."