This story may possible to happen only if mbappe will able to leave from there with free agent. As long as the club is not let mbappe to leave with free agent and it's just a dream to see him join in barcelona. Mbappe has been also rumored reached pre agreement with real madrid about moving there once he will able to leave from the club with free agent. There's no need to take mbappe. It will be only making the club even closer to the FFP. It's impossible to happen. Talking about mbappe and barcelona have same meant talk about a dream that will never happen.
Given the appetites of the Mbappe family, even leaving Paris Saint-Germain as a free agent would not have helped Barcelona much, because then there are demands for the payment of 100 million to Mbappe himself as a signing bonus and also a salary of 50-60 million euros, which Real Madrid already seems to have agreed to. Barcelona, with its financial problems, Mbappe's salary alone is unaffordable in the current conditions. Moreover, even now Barcelona seems to need to sell several players in order to sign new players.