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The economic crisis that Barcelona is currently facing forces them to bring in free transfer players, that is the only alternative that Barcelona can take in order to maintain their finances. Signing Mbappe is definitely impossible, these rumors can never come true. Barcelona of course really want to have a player like Mbappe, but difficult financial conditions have kept Barcelona silent without making any breakthroughs in the conditions that are befalling Mbappe at PSG.
Not all of the players Barcelona have signed so far are free transfer players. Barcelona also brought in several players with high transfer values such as Lewandowski, Kounde, Raphinha and Ferran Torres. Indeed it was their signing last season, but Barcelona can still sign players for a good transfer fee, not for free.
But about Kylian Mbappe, that's highly unlikely. Barcelona cannot bring Mbappe to Camp Nou for financial reasons, even if Mbappe is brought in for free then Barcelona will also be overwhelmed by paying his high salary. Kylian Mbappe is not for Barcelona, nor is it for Real Madrid if another team makes a fantastic bid for PSG.