There are those within the French club who worry that that sort of determination, in certain lights, can take on the veneer of desperation. There is also an ever-present concern that perhaps P.S.G. is being taken for a ride, being used as a bargaining chip in Neymar’s efforts to secure more money, and more prestige, at Barcelona. They have been burned before: P.S.G.’s pursuit of Ronaldo never did benefit P.S.G., but it most certainly benefited Ronaldo in contract negotiations with Real Madrid.

That Khelaifi, the chairman of P.S.G.’s owner, Qatar Sports Investments, is willing to run that risk again indicates that his attraction to Neymar is not some mere vanity project; it is not simply a desire to express P.S.G.’s or even Qatar’s financial power; it is not the Galáctico thinking of Real Madrid, the expensive indulgence of a man or a club seduced by Neymar’s celebrity. At the figures currently being discussed, it is nothing so trifling. At half a billion dollars, it seems to be something closer to a necessity.

When Q.S.I. first invested in P.S.G. in 2011, its stated aim — according to Khelaifi himself — was to win the French championship “for the next three years” and to become “competitive” in the Champions League.

By most measures, that has been accomplished. Although Monaco won Ligue 1 last year, P.S.G. had picked up the four previous championships. And while P.S.G. was spectacularly eliminated by a Neymar-inspired Barcelona in the round of 16 of the Champions League in March, it had become a fixture in the quarterfinals in the years before that.

It wanted to go further, of course. “Our aim is to make the club an institution respected around the world,” Khelaifi said last year. “If we are going to make that happen, we have to win the Champions League. That will take the club to a new dimension. Any team that wins it is seen differently by everyone else.”

Still, progress had been made. Khelaifi was correct to assert that P.S.G. was now viewed by Europe’s biggest clubs as a “serious challenger” to win the competition. “Most of them want to avoid us in the last 16,” he said. “That is a mark of respect in itself.”