South Africa, who are training at Herzogenaurach in Germany, will play fellow finalists North Korea in Frankfurt on Thursday.
The Koreans have been preparing for their World Cup campaign in Spain.
South Africa have already scheduled another warm-up international against China in Frankfurt on April 28, at the end of their three week training camp in Germany.
A third match against Estonia, set for the weekend, has been called off because of flight cancellations across Europe, the South African Football Association said in a statement on Tuesday.
Parreira criticised his own association at the weekend for their failure to organise testing friendlies for his squad of locally-based players during their stay in Germany.
The association have been on a rollercoaster of ridicule in recent weeks, having scrambled to secure a training ground and accommodation for their team during the World Cup long after the other finalists had settled on their base camps.
South Africa botched plans to renovate a facility near Johannesburg airport, and are now sharing a facility with the Dutch in the city.
A bid to find several strong opponents for matches in the last week before the start of the World Cup on June 11 also hangs in the balance, despite Parreira's insistence the team needs tough games to round off their tournament preparations.
A match against Denmark is still being negotiated, Danish officials told Reuters on Tuesday, despite South Africa confirming the match for Johannesburg on June 5.
A match against Colombia on May 27 has also been announced by South Africa but not confirmed by their opponents.
