A win by two clear goals in their final Group H clash on Friday would seal a place in the second round for the Swiss while a narrow win or a draw could be enough depending on the result of the Spain-Chile clash.
Frei, the country's record goalscorer, told reporters at Free State stadium that he was 100 percent fit despite missing his team's shock opening 1-0 win against Spain and playing just 42 minutes in the 1-0 defeat to Chile. The skipper suffered an ankle injury just hours before his team boarded the plane for South Africa.
Frei said the team were delighted to go into the Honduras match with their fate in their own hands but he expected a strong challenge from the central Americans, who still have an outside chance to qualify themselves.
When asked whether Switzerland, who have netted just three times in their past seven internationals, would struggle to score the goals they needed he said: "We practice very hard. We score goals in our training units as well. We scored two goals against Greece both in the home match and in the away match [in qualifying] so I think we have got a very good argument for scoring two goals tomorrow."
"Over the past qualification round we conceded very few goals," he added, acknowledging the strength of the team's defence but saying: "We can also score lots of goals. We just have to make sure we do score and we feel comfortable about that.
"All the players are hot. They want to get the second victory. They want to give a sensational performance tomorrow in order to reach the round of 16 with glory," added Frei, who has netted 40 international goals.
The Swiss set a new FIFA World Cup record of 559 minutes played without conceding a goal until Chile breached their defence. Frei said it would be foolish to underestimate Spain regardless of their defeat to the Swiss.
"It would be disastrous not to look at Spain as a favourite. Just take a look at the players they have. Take a look at the football they play. I'm sure they are going to put their foot down."
Chile have a maximum six points, with Spain and Switzerland both on three points. Honduras, appearing in only their second FIFA World Cup finals, are yet to get off the mark. Chile have a goal difference of plus two, with Spain on plus one and the Swiss, who reached the last 16 in Germany in 2006 before crashing out on penalties to Ukraine, on zero.