Manchester City, Inter Milan, Atletico Madrid and Porto have already been sent packing, while both teams from Argentina – Boca Juniors and River Plate – have also been eliminated.
Brazil’s Flamengo and Botafogo fell at the last-16 stage, but the country’s remaining two sides hope to march on.
“This tournament is a priority in the way an Olympic athlete will do all of his training and programming to peak at a specific time,” Vickery tells BBC Sport.
“Certainly for Palmeiras, who really want to win it. This is an absolute priority for them and they have programmed to be at their peak now.”
Could the climate, which the Brazilian teams are used to, be helping give them an edge?
Both Chelsea boss Enzo Maresca and Manchester City manager Pep Guardiola have mentioned the extreme heat since the tournament started.
Chelsea trained in 37C before their 3-0 group win over ES Tunis in Philadelphia.
“It is almost impossible to train or to make a session because of the weather,” said Maresca last week, while Guardiola said before last Thursday’s match with Juventus that his players must be prepared to “suffer” in the challenging heat of Orlando.
The soaring temperatures across the United States have led to matches across the competition implementing water breaks during games.
But not all players have struggled in the heat.
“We’re used to it,” Botafogo right-back Vitinho, who spent two years at Burnley, said of the high temperatures.
Another factor to consider is that all four teams from Brazil had broken away from their domestic season, which runs from March until December, to take part.
While they appear fresh and sharp, teams from Europe went into the Club World Cup on the back of long seasons.
PSG’s first game against Atletico Madrid in Pasadena on 15 June came 15 days after their 5-0 mauling of Inter Milan in the Champions League final in Munich.
Vickery adds: “A few weeks ago the Flamengo president was saying to a mate of mine ‘we’re flying in mid-season’.
“For the European clubs… is it the end of their season? Is it pre-season? The European clubs, their planning hasn’t been to peak now.”
Vickery believes there is something else to factor into the conversation about Brazilian clubs doing well.
“There is more money in Brazilian football [than before]” he says. “The standard has risen over the last few seasons. One reason is because of the influx of foreign coaches.
“Of the four Brazilian clubs here – two have Portuguese coaches [Abel Ferreira – Palmeiras and Renato Paiva – Botafogo].
“There’s plenty of Portuguese and Argentine coaches in Brazilian football and it’s brought more ideas. Even Filipe Luis, the Brazilian coaching Flamengo, his back-up staff are all Spanish.
“There’s an openness to new ideas that there wasn’t a few years ago.”
Mendonca adds: “The timing of this competition is very good for South American teams. They are in the middle of their season, they are very well prepared physically.
“They have better conditions now to keep their talented players and even bring back some players. Flamengo, for example, signed Jorginho after leaving Arsenal, while Danilo and Alex Sandro have come from Juventus.
“Also Botafogo, they have kept Igor Jesus for this competition. After this he will go to Nottingham Forest.
“These are aspects that explain why Brazilian teams are performing very well.”
