The France international was repeatedly linked with a move to the Santiago Bernabeu during the most recent transfer window.
Madrid are reported to have had three bids turned down for the France international in July and August, the last one said to be worth up to €200million.
Speaking about his future in detail for the first time, Mbappe confirmed in an interview with RMC Sport, which will be released in full on Tuesday, that he does not intend to sign a new deal at the Parc des Princes.
"I asked to leave," he said. "From the moment where I did not want to extend, I wanted for the club to receive a transfer fee so that they could bring in a quality replacement.
"It's not for me to judge, but my position was clear. I said that I wanted to leave and I said it quite early."