World Cup-winning attacker Mbappe has reportedly agreed personal terms to make a free-transfer switch to Madrid after his Paris Saint-Germain contract expires next month, though the Ligue 1 champions still hope to persuade him to stay.
The 23-year-old, who has scored 168 goals and supplied 77 assists in 216 games in all competitions for PSG, had also been linked with a switch to Barca.
However, the Catalan giant's president insists the club would not have been willing or able to get anywhere near his demands.
"There are things that even if we had the money to do it, we wouldn't because it distorts our wage bill and that cannot happen again. It is something we are instilling in the club in all areas," Laporta said.
"We can't go past a certain level of spending. Mbappe is asking for 40-50 million [euros] net. He wants 50 [million euros] net. Mbappe is at the highest level but hasn't won the Champions League. That must also be taken into account.
"We will not talk about salaries of 25, 30 or 40 [million euros] net. It would be offensive to players who are expected to be a reference in world football and are just starting out at Barcelona. We are not going to do that, nor do we want to."
Barca has been tipped to sign another of European football's elite strikers in the form of Robert Lewandowski, though.
Lewandowski does not wish to extend his Bayern Munich contract, which has a year to run, and he could become available for a transfer before the start of the 2022-23 season.
Asked if the Poland international will sign for Barca, Laporta said: "Let's let the football management and technical secretariat work. I don't want to answer in detail.
"We are working to be more competitive, but it's not easy due to the economic situation. We are working to clean up the club's finances. Then we can do things.
"I hope to be able to say that in a year we have largely cleaned up the club's finances. If we manage to clean it up, all the operations we are contemplating will be able to be dealt with."
A departure for Frenkie de Jong could be one way Barca look to raise funds, but Laporta was unwilling to divulge much when asked about the Netherlands midfielder.
"There are Barcelona players who are coveted on the market and we will do what is best for Barcelona," he said.
"If we manage to clean up the club's finances, we will have fair play, cash … I don't know if there will be sales."