The Pole hit four goals against Madrid in the Champions League semi-final first leg last season, which led then-coach Jose Mourinho to send a text message asking the striker to join him at his next club, which proved to be the Blues.
"Yes, there was a situation like this with Jose Mourinho but I wouldn't like to talk about it much," Lewandowski told The Sun.
"It was a private conversation so I don't want to make big things out of it. I can confirm I spoke to him.
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"It is always nice to talk to him but it is not the first time I had such a situation."
The 24-year-old was also lined up by former United manager Sir Alex Ferguson, though a move did not come to fruition because the forward had unfinished business at Signal Iduna Park.
"One year earlier I also spoke to Sir Alex Ferguson and that was definitely a great feeling," he added.
"The retirement of Sir Alex didn't affect my decision not to come to England. He spoke to me one year ago. It was not at a good time. I knew I still had something big to achieve in Dortmund before I joined a bigger club."
Lewandowski looks set to join Bayern Munich after the current season following Dortmund's refusal to sanction a move this summer but he has hinted that Real Madrid also entered into his thinking after he was approached by club president Florentino Perez following the second leg of the Champions League semi-final.
"It was in the office near the dressing room at the Santiago Bernabeu straight after the match. We spoke to each other briefly and ... OK, let's just say we spoke," the forward remarked.
"I didn't say 'no'. I was mostly listening to Mr Perez."