Brazil were criticised for some unconvincing play in the group stages and they only scraped through to the last eight after a nail-biting penalty shootout win against Chile.
But Scolari insisted his team were destined to win the World Cup before the tournament started and he is sticking by his words.
"Do we have one hand on the cup? Yes," the Brazilian said in a fiery press conference on the eve of the match.
"Don't forget those statements (I made about winning the World Cup before it started). They were all fantastic. Those statements could not be any different now.
"We are going on to the fifth step now. There are seven in total."
Brazil go into the match with criticism from some of the nation's biggest names still ringing in their ears. Zico and Carlos Alberto have led the criticism of Scolari's squad in recent days. Of particular annoyance to the two greats is the outpouring of emotion shown by the current squad at this World Cup.
Neymar, Julio Cesar and David Luiz all broke down in tears after the shootout win against Chile while Neymar also looked overcome with emotion when he sang the national anthem earlier in the tournament.
Carlos Alberto, Brazil's 1970 World Cup-winning captain, said recently: "The team is crying when they're singing the national anthem, when they get hurt, when they take penalties. Stop crying!"
Brazil's psychologist Regina Brandao visited the squad at their Teresopolis base on Tuesday, but Scolari denied that was anything out of the ordinary.
"It was scheduled and organised. Please stop thinking (otherwise)," the former Chelsea manager snapped when asked about Brandao's visit.
"I admire psychologists. She has participated in a very nice way. That's it. The players love to talk. She isn't even paid anything to do this."
Next in Scolari's sights were a bunch of disgruntled Brazilian journalists who questioned why they were excluded from a briefing with him at the training ground earlier this week.
He said: "I can't talk to all of you. I just sat down with a few people. If you don't like it, go to hell."
The one thing Scolari has to be happy about is the fact that Neymar is fit and ready to take on Colombia.
The Barcelona star suffered knee and thigh injuries during the bruising battle against Chile, but he is ready to go.
Scolari will have to make at least one change for the quarter-final though as Luis Gustavo is suspended.
Colombia defender Pablo Armero has laughed off suggestions that Brazil are vulnerable.
Despite topping Group A and reaching the last eight, the host nation have struggled to live up their billing as tournament favourites, failing to score against Mexico in their second game and only overcoming Chile in the round of 16 on penalties.
Nonetheless, former West Ham defender Armero does not believe Luis Felipe Scolari's side are struggling, emphasising the quality on display in the tournament and the level of determination in each team.
"Brazil are not weak, it's just that every team here wants to go as far as possible, we've seen that since the start of the World Cup," Armero told reporters.
"Every team wants to win and no-one is hiding. Also, they were up against Chile, who have great players."
By contrast, Colombia have exceeded all expectations in their first World Cup since 1998, winning all four of their games and scoring 11 goals.
And Armero emphasised that his team would not be content to go home at this stage.
"We are working so we can go as far as possible," he said.
"From the first game we knew it wasn't going to be easy, our attitude has been to go step by step.
"We haven't come here to go for a walk in the park. We've come here to give everything and go for glory."
The game will see a duel between Colombia forward James Rodriguez, who leads the scoring charts in the tournament with five goals, and Brazil's star man Neymar, who has scored four times.
Armero admitted his team would be paying special attention to the Barcelona forward, and is confident Colombia can knock the hosts out of the World Cup, as long as they play for each other.
"To nullify Neymar the whole team needs to help each other out in trying to mark him," he said.
"We need to stay united and not lose our focus. We are a compact team and we know that when we play together we get results."
- Sports & Recreation