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The 22-year-old French superstar has become the linchpin of PSG's attacking talent since his stunning permanent move from Monaco for £165.7m.
However, Mbappe's future in the French capital remains uncertain ahead of his contract expiring in June 2022.
The PSG forward has been heavily linked with a sensational move to Real Madrid for some time, with Florentino Perez refusing to rule out the chance to sign Mbappe.
Di Meco, 57, has now suggested that PSG must play hardball with Mbappe should he refuse to commit his future to the Ligue 1 side.
The former France international told RMC Sport: "The problem in this story is that by letting him go into the last year of his contract, he is the one who holds the cards.
"What you can do when you are PSG and you are powerful is say: 'You don't want to continue [with us]? Well, you can stay on the bench all year.'
"Paris has the means to do it. And by doing that, you show the guys who arrive that they cannot run the show."
Mbappe enjoyed a successful goalscoring season with PSG as he scored a whopping 42 times in 47 appearances across all competitions.
However, the Frenchman's 27 goals in France's top-flight domestic league weren't enough to stop PSG from conceding the Ligue 1 title to Lille.
Mbappe also endured a disappointing summer with France at Euro 2020 as he failed to score once for the 2018 World Cup champions.
The France international's woes were epitomised with his decisive spot-kick miss against Switzerland, with Didier Deschamps' men crashing out of the Euros in the last 16.
Mbappe has since released a heartfelt apology to fans, but he vowed that France would bounce back "even stronger for the next challenges."
Despite the uncertainty surrounding Mbappe's PSG future, Nasser Al-Khelaifi has firmly ruled out any intention of selling the former Monaco star.
The PSG president told L'Equipe in June: "I will be clear, Mbappe is going to stay in Paris.
"We will never sell him and he will never leave on a free [transfer]. Mbappe has everything he needs in Paris.
"Where can he go? What club, in terms of ambition, can compete with PSG today? All I can say is that things are going well and I hope we can reach an agreement [on a new contract].
"This is Paris, this is his country. He has a mission, not only to play football, but to promote Ligue 1, his country and his capital."
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