Perreira had in mind not just 1994, when his vilified team won in the United States, but 2002, when France and Argentina were favourites and Brazil, following a desperate qualifying campaign, outsiders. In 1982 and 1998, however, when they were highly fancied, they failed.
In Brazil the saying is, "We can only beat ourselves", said Tim Vickery, a Rio de Janeiro-based journalist for the BBC and World Soccer among others. "That's wrong. They are not unbeatable. They won only half of 18 qualifying matches. After the group stages the World Cup is a knock-out and there are 15 teams who, on a good day, can beat Brazil, as Mexico did in the Confederations Cup."
Brazil have reached the past three finals but, notes Vickery, progress has not been smooth. "The Dutch rocked them in '94 and should have walloped them in the '98 semi [Brazil won on penalties]. In 2002 they could easily have lost to Belgium [who had a goal harshly disallowed at 0-0]."
Vickery still believes Brazil are serious contenders, just not certs. He added: "It is in Europe and in France they struggled against European opposition, losing to Norway and France and having problems with Scotland, Denmark and the Netherlands."
That aspect is countered by Walter Smith, Scotland's manager. "I back Brazil," he said. "It takes something special for a country to win the World Cup in another continent and Brazil have got that. It helps that their best players are based in Europe."
Mike Collett, football editor at Reuters, who watched Brazil win the Confederations Cup in Germany last summer, agreed: "It doesn't matter that the tournament is in Europe," he said. "All their players are based there. The climate, the culture, the food, all the things that used to be an issue are now second nature."
But if Perreira is right - and any team which has Roque Junior as back-up centre-half cannot be perfect - who else is in the frame? "Italy, and for that matter, Germany, will give Brazil a run for their money," added Smith, whose Scotland team were in Italy's qualifying group.
Craig Brown, the former Scotland manager, is less convinced. "I saw both games against Scotland and Italy were very disappointing," he said. "They looked a collection of individuals whereas they used to be a tightly drilled team with great camaraderie.
"In Euro 2000 I watched their match against Belgium. Alessandro Del Piero, the golden boy, had been dropped for Francesco Totti, which was a big shock. Totti scored the opening goal and I looked to the bench and Del Piero was the first one off it to celebrate. That showed a really good team spirit. Then in the semi-finals they went to penalties against the Dutch and linked arms on the halfway line. That's common now but they were the first team I saw do it. But in Portugal last summer key players appeared to be playing for themselves and they still seem disjointed."
Besides Brazil, Brown fancied Ukraine and the Netherlands. "They are the team of the moment," he said of the Dutch. "Marco van Basten looks to have eliminated the infighting which bedevilled them in the past. I remember playing them just before they went to USA '94. Ruud Gullit had an argument with Dick Advocaat at half-time and just walked out. It was his last international."
Rob Fleur, of Dutch National Radio, explained: "Van Basten says he wants the best squad, not the best players. He has admitted there are better players around than the ones he is selecting but he wants a team in which no one says, 'I'm the best'. At Euro 2004 Dick Advocaat gave in when Clarence Seedorf said, 'I should be the No 10. I've won the most'. Now Seedorf and Patrick Kluivert are history.
"It is a very young team, with only a few experienced players like Phillip Cocu, Edwin van der Sar and Giovanni van Bronckhorst. And Van Basten has only one year's experience as third coach at Ajax." Fleur backed Brazil and Germany. "They always do well in tournaments, wherever they are, and this time they are hosts."
Collet agreed: "The fans got right behind them in the summer, it was incredible. And they have some good players in Lukas Podolski, Christoph Metzelder and Per Mertesacker. But my dark horses are the Netherlands. They have a developing team with good young players."
Outside Europe, Argentina are seen as contenders, though Vickery noted that Jose Pekerman was reviewing his players and tactics, but the qualification of four virgin African nations, while a romantic story, is expected to mean early departures.
And what of England?
"You cannot win World Cups with a midfield which is all generals and no soldiers and that is what England have," Fleur said.
Collett added: "I can't see England stringing together six or seven good enough performances. They seem to lack belief when it comes to major tournaments, unlike Germany who always seem to believe they can win it even when they have an ordinary team."
Brown dissented. "It is fashionable to have a go at the manager, but anyone can have a result like England did in Belfast," he said. " Liechtenstein were winning 1-0 at half-time in Portugal at the weekend.
"England have quality and, whatever people say, Sven Goran Eriksson is no fool. He has a tremendous record over his career and the spirit in the camp is good. You never see any player criticise him, even those, like Paul Scholes, who have retired or David James, who's been dropped. That's a good sign.
"A good manager, with good staff and good players: they have a great chance."
The battle for remaining places
Five berths are still to be decided for the World Cup finals through play-offs. The winner of each play-off will qualify.
The pairings for three play-off matches involving European teams will be drawn today at the Fifa headquarters in Zurich. The teams are Czech Republic (world ranking 4), Norway (37), Slovakia (45), Spain (8), Switzerland (38) and Turkey (12). With superior world rankings the Czech Republic, Spain and Turkey will be seeded when the draw is made.
REST OF THE WORLD
Australia, the Oceania winners, will face Uruguay, the fifth-placed South American team.
Bahrain, the Asian zone's fifth-best team, will play Trinidad & Tobago, the fourth-best team from Concacaf.
All play-off matches will be played over two legs on 12 and 16 November.
How the qualifiers' chances compare to official Fifa rankings
Previous World Cups 17, Best finish Winners, Fifa ranking 1st
Everybody's favourites. Adriano or Robinho? A choice any manager would envy. But is the defence sound?
Star man: Ronaldinho
2: THE NETHERLANDS
(7, final, 2nd)
Marco van Basten is a miracle worker. With minimal experience he has forged the argumentative Dutch into a unit, developed young talent, and won matches. Can it last?
Star man: Edwin van der Sar
(13, winners, 3rd)
Gone off the boil since qualifying by drubbing Brazil, but a quality squad enhanced by Lionel Messi.
Star man: Juan Riquelme
(15, winners, 15th)
Hosts always do well in World Cups, as do the Germans, but have failed to convince in recent friendlies.
Star man: Michael Ballack
(11, winners, 6th)
Zidane rescued them in the qualifiers, but will he be as fresh in June?
Star man: Zinedine Zidane
(3, semi-finals, 9th)
Any team with a rejuvenated Figo, a maturing Ronaldo and Carvalho in defence cannot be discounted.
Star man: Ricardo Carvalho
(11, winners, 11th)
With Rooney, anything is possible.
Star man: Wayne Rooney
(10, final, 10th)
Difficult to beat. A dark - or rather blond - horse.
Star man: Zlaten Ibrahimovic
(0, n/a, 39th)
At last a world stage for Shevchenko. Another dark horse.
Star man: Andrei Shevchencko
(15, winners, 13th)
What below Ukraine and Sweden? Controversial, but successive failures have knocked belief. Results were more impressive than performances in qualifying.
Star man: Andrea Pirlo
(2, semi-final, 24th)
Technically gifted and qualified smoothly. Lack the stars of past, but a solid unit which plays with head and heart.
Star man: Darijo Srna
12: UNITED STATES
(7, semi-finals, 7th)
Functional rather than spectacular but that took them to the last eight in 2002.
Star man: Landon Donovan
13: IVORY COAST
(0, n/a, 50th)
Drogba, Kolo Touré, Aruna Dindane and St Etienne's Zokora provide a thread of quality.
Star man: Didier Drogba
(12, qtr-final, 5th)
Beat Brazil in the Confederations Cup.
Star man: Jared Borgetti
15: SERBIA & MONTENEGRO
(0, n/a, 48th)
Tightest defence in Europe, conceding one goal in 10 qualifiers.
Star man: Meteja Kezman
(0, n/a, 62nd)
Strong midfield includes Essien and Appiah.
Star man: Michael Essien
(2, 2nd rd, 16th)
Star man: Hidetoshi Nakata
(6, semi-finals, 17th)
Out of their depth.
Star man: Maciej Zurawski
(2, gp stage, 18th)
Will utilise a core of Bundesliga players.
Star man: Mehdi Mahdavikia
(3, gp stage, 23rd)
Star man: Hatem Trabelsi
(6, 2nd rd, 34th)
Qualifying was an achievement.
Star man: Roque Santa Cruz
22: SOUTH KOREA
(6, semi-final, 26th)
A miracle if they match heights of 2002.
Star man: Ji-Sung Park
23: COSTA RICA
(2, 2nd rd, 19th)
Unlikely to progress.
Star man: Paulo Wanchope
24: SAUDI ARABIA
(3, 2nd rd, 28th)
Star man: Sami al-Jaber
(1, gp stage, 33rd)
Star man: Delgado
(0, n/a, 65th)
Star man: Maieco
(0, n/a, 54th)
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