Parreira said a recent 4-0 friendly win over Thailand and increased intensity in training had given him a positive feeling.
South Africa, drawn with France, Mexico and Uruguay in Group A, are seeking to avoid becoming the first World Cup hosts to fail to get past the first round of their tournament.
"My stomach tells me we are going to do well. I have a very positive feeling. Every time I see them (the players) train, they are looking better and better. Every day they spent together, you can see the improvement," he told a media briefing on Sunday.
South Africa play Bulgaria in Soweto on Monday as they continue their preparations for the opening World Cup game against Mexico in Johannesburg on June 11.
"The idea is to take it step-by-step but always go forward, never going backwards," Parreira said.
"We want to keep improving on every performance and then we should have the confidence that we are going to do well at the World Cup."
South Africa then face Colombia on Thursday and Parreira said he wanted another international on May 31 before his team's final warm-up game against Denmark on June 5 in Pretoria.
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