Klopp is the same, having criticized England’s “obsession” with transfers this month. Both men, however, are exceptions. For the most part, the colossal sums spent by English clubs on new players are seen as something to be celebrated, evidence of the Premier League’s potency. Every year on deadline day, the television channel Sky Sports News keeps a tally of the 20 clubs’ gross outlay in the corner of the screen. The sight of the black-on-gold totalizator creeping ever higher is treated with the sort of delight more commonly associated with charity telethons. Soccer treats buying as a virtue.

And yet Schweinsteiger and Balotelli — like Joe Hart, the Manchester City goalkeeper who was unceremoniously demoted by Pep Guardiola and is on the verge of a loan move to Torino, which finished in 12th place in Italy’s Serie A last season — offer a sober reminder that there is a flip side to this unrivaled financial firepower.

“There are a handful of teams in the Premier League who are under a lot of pressure to buy players,” said José María Cruz, the chief executive of the Spanish team Sevilla. “They pay a lot of money, and so they need an immediate return on that investment: They need the players to perform straightaway.

“If they do not, they are already looking for a replacement after three or six months. But trying to offload the players who are no longer wanted is very complicated because the salaries are so high. They are not realistic for most clubs in Europe.”

Sevilla, for example, has the fifth-highest player payroll in Spain. Thanks to a run of three successive Europa League victories and qualification for the Champions League, Cruz can approve better salaries than most of his peers. The Premier League market, though, is still too expensive.

That is certainly the case with Schweinsteiger and Hart, both of whom earn more than $200,000 each week. Balotelli makes substantially less, but his £90,000-a-week wages (about $118,000) still rule out a host of teams, particularly for a player so weighed down with baggage.

More troubling, even the likes of Emmanuel Rivière, an unremarkable French striker no longer in the plans at relegated Newcastle, are so richly compensated by their current teams that it is difficult to shed them. At £40,000 a week — just over $52,000 — Rivière earns almost twice as much at Newcastle as any of the clubs who might be tempted to sign him could afford to pay. As Wenger says, there are now effectively “two markets, one for the English clubs and one for the rest of Europe.”