Sources told ESPN on Tuesday that Madrid saw their €160 million offer for the 22-year-old's rights rejected, but were hopeful of agreeing to a deal before the transfer window closes on Aug. 31.
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"Kylian Mbappe wants to leave, that seems clear," Leonardo told French outlet RMC on Wednesday. "If he wants to leave, we are not going to keep him, but it will be done under our conditions.
"We have spoken a lot with Kylian and he always tells us the same thing. Kylian has always promised us that he would never leave the club on a free transfer."
Mbappe has a year left on his PSG contract and has refused multiple offers of a renewal, meaning the Ligue 1 club risk losing him on a free transfer in June 2022.
Speaking in a joint interview with four French media outlets and the Spanish newspaper Marca on Wednesday, Leonardo hit out at Madrid's approach to the negotiations, calling their behaviour "disrespectful, incorrect, illegal and unacceptable."
"Verbally we've said no to Madrid," Leonardo said. "We haven't received another offer. We've never wanted him to leave, we've never imagined it, we made a very important offer and an even better second one to renew.
"The player gave his word that he wouldn't leave PSG for free but in the end that looks like the strategy, for him to leave for free."
PSG signed Mbappe from AS Monaco for €180m in 2018 following a year loan and Leonardo said they were not prepared to offload him for lower than that.
"We aren't going to get rid a player for less than we paid for him at 18 years old," he added. "We have to pay an amount we owe to Monaco, and we don't consider the offer to be sufficient."
Sources have told ESPN that Madrid are considering another bid for Mbappe before the transfer window shuts.
Madrid could wait until next summer to sign the forward but multiple sources have told ESPN that they have decided to do everything in their power to show the player the club are "determined and committed" to signing him.
Sources have told ESPN it would take an offer of around €200m to make PSG consider accepting a deal, and Mbappe remains Florentino Perez's main target ahead of Borussia Dortmund striker Erling Haaland.
"Kylian is the centre of our project but he isn't above it," Leonardo added. "If he stays or he goes, it will always be with our conditions. If he wants to go, he'll go, but with our conditions like any other player. We won't change the plan a week from the close of the market.
"There's been a global strategy for the last two years to arrive at this moment, to make an offer with a week until the end of the market that they know we won't accept, and say: 'Oh well, we've tried and they didn't want to and we'll have the right to sign him for free.'
"Our objective is for him to stay and renew. Madrid have made an offer. And Mbappe has always promised that he would never leave the club for free. Let's see what happens in a year's time... honestly, we're not happy."