The attacker's representative has revealed that the Santiago Bernabeu side was keen to the Poland international to La Liga
The Poland international signed a five-year deal with the Bundesliga champions Saturday to bring a protracted transfer saga to an end.
However, Barthel has revealed that Madrid was keen to sign Lewandowski, too, and was willing to go far for the 25-year-old.
"There was an immoral offer from Real Madrid," the striker's representative was quoted as saying by Spiegel Online.
Madrid was reportedly willing to offer Lewandowski an annual salary of 9.5 million euros plus an additional 10 million euro signing fee, but Barthel has made it clear that they never considered breaking their promise to Bayern.
"We listened to their offer out of respect for such a big club. But breaking our word never crossed our mind," he said.
Lewandowski has been in sublime form for Dortmund this season, scoring 11 goals in 17 Bundesliga appearances.