SunSport exclusively revealed the pictures of the Poland international meeting with Zahavi at a swanky Izakaya Asian Kitchen in Munich.
Bayern are reluctant to sell their top scorer who has three years left on his contract.
But Lewandowski has been planning his exit strategy since February when he teamed up with his new agent.
The Israeli agent, 74, has close ties to Chelsea and was allegedly behind Neymar’s £198million move to PSG from Barcelona.
Zahavi said at the time Lewandowski became his client: “I am glad that Robert decided to co-operate with me.
“I will do everything to work well in his name.
“He is a great footballer. He is the best striker in the world. Therefore, it is not surprising that I have signals about the interest of his person in all major clubs.
“Will Robert go to Real Madrid? We’ll see. Now it’s time for me to do my job.”
The ex-Borussia Dortmund hotshot registered 29 goals for Bayern in the 2017/18 campaign and became the first non-German to top the scoring charts on three separate occasions.
In contrast, Real’s main striker Karim Benzema has scored just five goals in LaLiga all season.
The Champions League finalists appear to accept the fact they will not be signing Tottenham’s Harry Kane this summer and Lewandowski is the man they want to get in the mean time before they make a firm approach for Kane.
However, Chelsea are also keen to land Lewandowski as they’re attacking options look rather limited with Alvaro Morata struggling for form.
Bayern chief Karl-Heinz Rummenigge said the club’s star striker is not going anywhere.
He said: “Nobody needs to worry about Robert Lewandowski and his relationship with Bayern Munich. We have a very good one.
“We know what we have in Robert Lewandowski.
“I’m very happy that we still have such a long-term contract.
“No one needs to think about it. He will play for Bayern Munich next season, too.
“He’s one of the best centre-forwards in the world. The numbers prove it every year.
“If he doesn’t score a goal in a few games now and then, that’s not a problem.”